User andreas holmstrom - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T01:46:22Z http://mathoverflow.net/feeds/user/349 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126699/status-of-beilinson-conjectures/126714#126714 Answer by Andreas Holmstrom for Status of Beilinson conjectures? Andreas Holmstrom 2013-04-06T16:12:59Z 2013-04-06T16:12:59Z <p>The <a href="http://www.math.jussieu.fr/~nekovar/pu/mot.pdf" rel="nofollow">survey of Nekovar</a> tells you what was known about the Beilinson conjectures in the early 90s. Other surveys/introductions from that time include <a href="https://www.dpmms.cam.ac.uk/~ajs1005/preprints/d-s.pdf" rel="nofollow">Scholl-Deninger</a>, <a href="http://archive.numdam.org/ARCHIVE/SB/SB_1984-1985__27_/SB_1984-1985__27__237_0/SB_1984-1985__27__237_0.pdf" rel="nofollow">Soulé</a>, Ramakrishnan (in <a href="http://www.ams.org/books/conm/083/" rel="nofollow">Contemporary mathematics 83</a>), and the volume edited by Rapoport, Schappacher and Schneider (introduction <a href="http://wwwmath.uni-muenster.de/u/pschnei/publ/beilinson-volume/preface.pdf" rel="nofollow">here</a>, all articles <a href="http://wwwmath.uni-muenster.de/u/peter.schneider/publ/beilinson-volume/" rel="nofollow">here</a>). Since then, not a lot has happened I think. There is a fairly recent article of Otsubo with some results for Fermat curves (<a href="http://www.degruyter.com/dg/viewarticle/j%24002fcrll.2011.2011.issue-660%24002fcrelle.2011.083%24002fcrelle.2011.083.xml" rel="nofollow">published version</a>, <a href="http://front.math.ucdavis.edu/0909.3002" rel="nofollow">arXiv version</a>). There is a nice reformulation of the conjectures in terms of Arakelov motivic cohomology, by Jakob Scholbach (see articles on <a href="http://wwwmath.uni-muenster.de/u/jakob.scholbach/" rel="nofollow">his webpage</a>). You might also want to check out some of the articles of <a href="http://www.few.vu.nl/~jeu/" rel="nofollow">Rob de Jeu</a> and his coauthors. In addition, there have been various attempts at new descriptions of the Beilinson regulator, most recently by <a href="http://front.math.ucdavis.edu/1209.6451" rel="nofollow">Bunke and Tamme</a> (their work will by the way be the topic of a <a href="http://www.gk1821.uni-freiburg.de/summer13" rel="nofollow">summer school in Freiburg</a> in July), but this does not in itself imply any progress on the Beilinson conjectures themselves.</p> <p>If you are interested in recent progress on special values in general, there are other areas where more exciting things are happening. Search for work on the Birch and Swinnerton-Dyer conjecture, the Equivariant Tamagawa number conjecture, and Weil-etale cohomology (starting point for Weil-etale: <a href="http://www.math.uni-muenster.de/reine/u/bmori_01/" rel="nofollow">webpage of Baptiste Morin</a>).</p> http://mathoverflow.net/questions/686/handling-arxiv-feeds-to-avoid-duplicates Handling arXiv feeds to avoid duplicates Andreas Holmstrom 2009-10-15T23:51:56Z 2013-01-04T06:09:45Z <p>I subscribe to feeds from the <a href="http://front.math.ucdavis.edu/math" rel="nofollow">arXiv Front</a> for a number of subject areas, using <a href="http://www.google.com/reader" rel="nofollow">Google Reader</a>. This is great, but there is one problem: when a new preprint is listed in several subject categories, it gets listed in several feeds, which means I have to spend more time reading through the lists of new items, and due to my slightly dysfunctional memory, I often download the same preprint twice. Is there a way to get around this problem, by somehow merging the feeds, using a different arXiv site, or using some other clever trick?</p> <p>(Hope this is not too off-topic, I think a good answer could be useful to a number of mathematicians. Also, I would like to tag this "arxiv" but am not allowed to add new tags.)</p> http://mathoverflow.net/questions/110658/fubini-theorem-for-hocolim/110743#110743 Answer by Andreas Holmstrom for Fubini theorem for hocolim. Andreas Holmstrom 2012-10-26T09:45:59Z 2012-10-26T12:05:06Z <p>You might also be interested in chapter III of the paper <a href="http://arxiv.org/abs/math/0110316" rel="nofollow">Homotopy theory of diagrams</a>, by Chacholski and Scherer.</p> http://mathoverflow.net/questions/110612/background-reading-for-proving-irrationality-of-real-numbers/110742#110742 Answer by Andreas Holmstrom for Background Reading for Proving Irrationality of Real Numbers Andreas Holmstrom 2012-10-26T09:34:44Z 2012-10-26T09:34:44Z <p>You might be interested in the concept called periods. Quid already mentioned the work of Waldschmidt, but see also <a href="http://en.wikipedia.org/wiki/Ring_of_periods" rel="nofollow">Wikipedia</a>, and in particular the link at the bottom to the article of Kontsevich and Zagier.</p> http://mathoverflow.net/questions/105190/power-series-expansions-of-l-series/109249#109249 Answer by Andreas Holmstrom for Power series expansions of $L$-series Andreas Holmstrom 2012-10-09T19:34:55Z 2012-10-09T19:34:55Z <p>There is a related conjecture for the L-function attached to certain Galois representations, due to Colmez and stated in the beautiful survey paper <a href="http://www.ihes.fr/~maxim/TEXTS/Periods.pdf" rel="nofollow">Periods</a> by Kontsevich and Zagier (see section 3.6). This survey paper refers to an Annals paper of Colmez: Périodes des variétés abéliennes à multiplication complexe (<a href="http://www.jstor.org/stable/2946559" rel="nofollow">Jstor link</a>), and to some papers of Hiroyuki Yoshida.</p> <p>There is also a book by Hiroyuki Yoshida called Absolute CM-periods, where some of this might be discussed. </p> <p>I have no idea whether this is related or not to the Rössler-Maillot/Kudla story mentioned above in the comments.</p> <p>The conjecture as stated by Kontsevich and Zagier is for a Galois representation sending complex conjugation to minus the identity matrix. This is a rather restrictive condition, and Kontsevich-Zagier also state (without explanation) that "in general, one does not expect any interesting number-theoretic property for subleading coefficients".</p> http://mathoverflow.net/questions/105575/finiteness-of-stable-homotopy-groups-of-spheres Finiteness of stable homotopy groups of spheres Andreas Holmstrom 2012-08-26T21:33:13Z 2012-08-26T22:53:49Z <p>Since the work of Serre in the early 50's on homotopy groups of spheres, it is known that the homotopy group $\pi_k(S^n)$ is finite, except when $k=n$ (in which case the group is $\mathbb{Z}$), or when $n$ is even and $k=2n-1$ (in which case the group is the direct sum of $\mathbb{Z}$ and a finite group). As a consequence, the stable homotopy groups $\pi_k^s$ are finite groups for $k>0$, and $\pi_0^s \cong \mathbb{Z}$. </p> <p>The work of Serre was done before anyone knew about stable homotopy theory and chromatic methods, and this makes me wonder about the following questions. </p> <p>Question 1: Is it possible to use methods from stable/chromatic homotopy theory to prove finiteness of stable homotopy groups of spheres directly, without having to compute any unstable homotopy groups of spheres? </p> <p>Question 2: Is there any philosophical or conceptual reason for why these groups should be finite?</p> http://mathoverflow.net/questions/94467/math-circles-video-lectures-for-school-children/97110#97110 Answer by Andreas Holmstrom for math circles video lectures for school children? Andreas Holmstrom 2012-05-16T11:20:19Z 2012-05-16T11:20:19Z <p>You might want to check out the <a href="http://www.khanacademy.org/" rel="nofollow">Khan Academy</a>. They have a lot of videos on all levels of school mathematics.</p> http://mathoverflow.net/questions/80403/number-fields-with-same-zeta-function/84589#84589 Answer by Andreas Holmstrom for Number fields with same zeta function? Andreas Holmstrom 2011-12-30T13:47:01Z 2011-12-30T13:47:01Z <p>Coming very late to the party, here is a small complement to Alex's excellent answer. There is a recent paper of Marcolli and Cornelissen (<a href="http://arxiv.org/abs/1009.0736" rel="nofollow">arXiv link</a>) which among other things discusses this question. The following two points give partial answers to the question posed here:</p> <ol> <li><p>If two number fields are Galois over $\mathbb{Q}$ and have the same zeta function, then they are isomorphic.</p></li> <li><p>In general, one can say something similar if one is willing to consider all twists of the zeta function by Dirichlet characters. More precisely, assume that there is an isomorphism between the Pontryagin duals of the abelianized Galois groups of the two number fields. Assume also that whenever two characters are identified under this isomorphism, the corresponding twisted zeta functions agree. Then the two number fields are isomorphic. See Theorem 2 in the paper linked above for more details. </p></li> </ol> <p>The introduction of the paper actually gives a rather good overview over criteria which can or cannot determine whether two number fields are isomorphic. </p> http://mathoverflow.net/questions/80903/is-the-free-r-module-on-a-sheaf-of-sets-still-a-sheaf Is the free R-module on a sheaf of sets still a sheaf? Andreas Holmstrom 2011-11-14T16:30:15Z 2011-11-14T17:09:47Z <p>Let $L$ be a sheaf of sets on some site $S$. Let $F$ be the presheaf obtained by composing $L$ with the free R-module functor, i.e. for any object $U$, we define $F(U)$ to be the free $R$-module on the set $L(U)$. Is $F$ a sheaf?</p> http://mathoverflow.net/questions/1291/a-learning-roadmap-for-algebraic-geometry/78457#78457 Answer by Andreas Holmstrom for A learning roadmap for algebraic geometry Andreas Holmstrom 2011-10-18T14:12:20Z 2011-10-18T14:12:20Z <p>There are a few great pieces of exposition by Dieudonné that I really like. The first two together form an introduction to (or survey of) Grothendieck's EGA. The second is more of a historical survey of the long road leading up to the theory of schemes. I am sure all of these are available online, but maybe not so easy to find.</p> <ul> <li>Algebraic geometry ("The Maryland Lectures", in English), MR0150140</li> <li>Fondements de la géométrie algébrique moderne (in French), MR0246883</li> <li>The historical development of algebraic geometry (available <a href="http://www.google.com/url?sa=t&amp;source=web&amp;cd=8&amp;ved=0CE0QFjAH&amp;url=http%253A%252F%252Fmathdl.maa.org%252Fimages%252Fupload_library%252F22%252FFord%252FDieudonne.pdf&amp;rct=j&amp;q=dieudonne%2520maryland%2520lectures&amp;ei=14SdTv_dDNS5hAfU7_idCQ&amp;usg=AFQjCNFAWXdvTVsnuYx17bprMse2cJO4gA&amp;cad=rja" rel="nofollow">here</a> or <a href="http://www.google.com/url?sa=t&amp;source=web&amp;cd=4&amp;ved=0CCkQFjAD&amp;url=http%253A%252F%252Fwww.math.ncc.metu.edu.tr%252Fcontent%252Fcourses%252Fprevious%252F2011spring%252Fmath526%252Ffiles%252Fdieudonne1.pdf&amp;rct=j&amp;q=dieudonne%2520maryland%2520lectures&amp;ei=14SdTv_dDNS5hAfU7_idCQ&amp;usg=AFQjCNFIsCGF94l4BIuABveWF704MYDkMw&amp;cad=rja" rel="nofollow">here</a>)</li> </ul> http://mathoverflow.net/questions/6394/lecture-notes-on-representations-of-finite-groups/6409#6409 Answer by Andreas Holmstrom for Lecture notes on representations of finite groups Andreas Holmstrom 2009-11-21T21:22:38Z 2011-06-28T15:28:05Z <p>Some material from the undergrad rep theory course in Cambridge: <a href="http://www.dpmms.cam.ac.uk/site2002/Teaching/II/RepresentationTheory/" rel="nofollow">Example sheets</a>, A <a href="http://tartarus.org/gareth/maths/notes/ii/Repn_Theory.pdf" rel="nofollow">recent set of notes</a> (by Martin), and a <a href="http://math.berkeley.edu/~teleman/math/RepThry.pdf" rel="nofollow">less recent (but very nice) set of notes</a> (by Teleman).</p> http://mathoverflow.net/questions/61852/a-question-on-k-1-of-an-elliptic-curve A question on K_1 of an elliptic curve Andreas Holmstrom 2011-04-15T18:32:21Z 2011-04-26T15:26:02Z <p>Consider an elliptic curve $E/ \mathbb{Q}$, with a regular model $\mathcal{E} / \mathbb{Z}$. We have (Beilinson regulator) maps $$K_1(\mathcal{E})^{(2)} \to K_1(E)^{(2)} \to H_D^3(E_{/ \mathbb{R}} , \mathbb{R}(2) )$$ from (an Adams eigenspace of) K-theory (with rational coefficients) to Deligne cohomology of $E$. Call the first map $\iota$ and the second map $r$. Note that this map does NOT lie in the index range where the Beilinson conjectures predicts that $r$ is an isomorphism on the image of $\iota$ after tensoring with $\mathbb{R}$. Now, is anything known at all about $r$ or $r \circ \iota$, for elliptic curves in general or for some specific curve/class of curves? Unless I am mistaken, the Deligne cohomology group in question is always a one-dimensional real vector space. My main question is the following:</p> <ol> <li>After tensoring everything with $\mathbb{R}$, is the the map $r \circ \iota$ zero or surjective??? </li> </ol> <p>I would also be interested in the following questions:</p> <ol> <li><p>Is anything known about the two K-groups here? Finite generation? Rank? Can you write down a nonzero element?</p></li> <li><p>Is the map $\iota$ injective? (This could be asked in much more generality for K-groups of regular models.)</p></li> </ol> <p>I'd be grateful for any hints, even those based on unproven conjectures.</p> <p>EDIT: Maybe one can approach this question from another point of view. I am quite sure that the following is true (have to check though). The cokernel of $r \circ \iota$ can be identified with the Gillet-Soulé arithmetic Chow group $\widehat{CH}^2(\mathcal{E}) \otimes \mathbb{R}$. Furthermore, this group is generated by arithmetic cycles of the form $(Z,g) = (0,\alpha)$, where $\alpha$ is a real harmonic $(1,1)$-form on the complex torus $E(\mathbb{C})$. So the question becomes: Do all arithmetic cycles of this form lie in the group generated by arithmetic cycles of the forms $(div(f), - \log \| f \|^2)$ and $(0, \partial u + \bar{\partial} v)$?</p> http://mathoverflow.net/questions/61763/zero-cycles-on-an-arithmetic-surface Zero-cycles on an arithmetic surface Andreas Holmstrom 2011-04-14T23:50:36Z 2011-04-15T01:47:56Z <p>Could anyone give a reference for the following statement, which I believe is true.</p> <p>"Let X be a regular scheme, flat over $Spec( \mathbb{Z})$, with fiber dimension $1$. Then the Chow group $CH^2(X)$ is finite."</p> http://mathoverflow.net/questions/61620/beilinsons-height-pairing-vs-neron-tate Beilinson's height pairing vs Neron-Tate Andreas Holmstrom 2011-04-14T01:46:48Z 2011-04-14T03:01:11Z <p>In the literature there are several different definitions of what is often referred to as Beilinson's height pairing (see for example section 4.3.8 of Gillet and Soulé's paper <a href="http://www.numdam.org/numdam-bin/fitem?id=PMIHES_1990__72__93_0" rel="nofollow">Arithmetic intersection theory</a>, and this <a href="http://hodge.mathematik.uni-mainz.de/~stefan/papers/cime.pdf" rel="nofollow">note</a> of Müller-Stach). The height pairing is supposed to generalize the <a href="http://en.wikipedia.org/wiki/Neron%25E2%2580%2593Tate_height" rel="nofollow">Neron-Tate height pairing</a>. Is there a precise statement in the literature where Beilinson's height pairing for an elliptic curve over $\mathbb{Q}$ is compared to the Neron-Tate pairing? </p> http://mathoverflow.net/questions/60107/describing-the-kernel-of-the-exponential-map-as-a-homology-group Describing the kernel of the exponential map as a homology group Andreas Holmstrom 2011-03-30T19:12:04Z 2011-03-30T20:58:14Z <p>I am reading Deligne: Hodge III, and am puzzled by a certain statement in section 10. If anyone could give a reference or a hint for how to prove this, I would be grateful. Maybe it is obvious and I just don't see why.</p> <p>We consider an extension $G$ of an abelian variety by a torus. Then Deligne claims that the kernel of the exponential map $Lie(G) \to G$ can be identified with $H_1(G, \mathbb{Z} )$. Why is this true?</p> http://mathoverflow.net/questions/53036/books-you-would-like-to-read-if-somebody-would-just-write-them/54386#54386 Answer by Andreas Holmstrom for Books you would like to read (if somebody would just write them...) Andreas Holmstrom 2011-02-05T02:59:39Z 2011-02-05T02:59:39Z <p><strong>Introduction to algebraic cycles.</strong></p> <p>With lots of examples...</p> http://mathoverflow.net/questions/54186/reference-learning-noncommutative-geometry-and-c-algebras/54385#54385 Answer by Andreas Holmstrom for Reference: Learning noncommutative geometry and C^* algebras Andreas Holmstrom 2011-02-05T02:55:33Z 2011-02-05T02:55:33Z <p>A while ago Lieven Le Bruyn put together a list called "Top 10 noncommutative geometry books for newbies", with a short description/review of each book. Check <a href="http://www.noncommutative.org/index.php/top-10-noncommutative-geometry-books-for-newbies/" rel="nofollow">this link</a>.</p> http://mathoverflow.net/questions/747/references-for-syntomic-cohomology References for syntomic cohomology Andreas Holmstrom 2009-10-16T15:28:23Z 2011-02-03T10:26:22Z <p>Could anyone point to good readable references for learning about syntomic cohomology?</p> http://mathoverflow.net/questions/34801/dirichlets-regulator-vs-beilinsons-regulator Dirichlet's regulator vs Beilinson's regulator Andreas Holmstrom 2010-08-06T22:35:32Z 2011-01-06T23:48:43Z <p>Consider a number field $F$ with ring of integers $O_F$. The Beilinson regulator can in this particular setting be viewed as a map from $K_n(O_F)$ to a suitable real vector space. Here $n$ is any positive odd integer. For $n \geq 3$, there is also another regulator map, defined by Borel, and Burgos has proved that the Borel regulator (suitably normalized) is twice Beilinson's regulator. For $n=1$, the Borel regulator is not defined (as far as I understand, correct me if I'm wrong), but we do have the original and most basic example of a regulator, which is that of Dirichlet.</p> <p>Question: Is there some form of comparison theorem between the Beilinson regulator and the Dirichlet regulator?</p> http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang If a colimit of distinguished triangles exists, is it also a distinguished triangle? Andreas Holmstrom 2010-07-26T00:49:27Z 2010-09-17T11:05:08Z <p>Consider the following situation in some triangulated category: We are given a collection of distinguished triangles $A_n \to B_n \to C_n \to A_n[1]$ indexed by the natural numbers, together with maps (in the obvious sense) from the n'th triangle to the (n+1)'st. If $A \to B \to C$ is the colimit of this system of triangles, is it also a distinguished triangle?</p> <p>It would be really interesting to have a proof or a counterexample, or possible a proof depending on some additional hypotheses on the triangulated category in question.</p> http://mathoverflow.net/questions/952/where-are-mathematics-jobs-advertised-if-not-on-mathjobs-e-g-in-europe-and-else Where are mathematics jobs advertised if not on mathjobs (e.g. in Europe and elsewhere)? Andreas Holmstrom 2009-10-17T22:55:40Z 2010-08-28T03:44:06Z <p>My impression is that in the US, there is a canonical place for finding math jobs, namely mathjobs.org. For those of us who live and apply for jobs elsewhere, life is more complicated, and searching for advertised academic mathematics jobs for example in Europe can be a real hassle, with loads of different sites, different systems, and some jobs apparently advertised only on the web page of the hiring institution, or one some obscure mailing list.</p> <p>So, where are academic math jobs advertised when they for some reason are not or cannot be on mathjobs.org? Of course I know of a few such places, but I am sure there must be many more.</p> <p>All answers welcome, this would help me and probably many others.</p> http://mathoverflow.net/questions/33561/sequential-colim-vs-sequential-hocolim Sequential colim vs sequential hocolim Andreas Holmstrom 2010-07-27T19:20:51Z 2010-07-28T04:01:08Z <p>Suppose we have some homotopical setting in which we can speak of homotopy colimits. The setting I have in mind at the moment is that of a compactly generated triangulated category with a model, but we could look at any model category or some other homotopical context. Let $A_0 \to A_1 \to A_2 \to \cdots$ be a system of objects indexed by the natural numbers. My question is if there are theorems of the form "under such and such hypotheses, hocolim $(A_i)$ agrees with colim $(A_i)$". </p> http://mathoverflow.net/questions/33556/do-homotopy-colimits-always-commute-with-homotopy-colimits Do homotopy colimits always commute with homotopy colimits? Andreas Holmstrom 2010-07-27T19:10:10Z 2010-07-27T19:27:41Z <p>Do homotopy colimits commute with homotopy colimits? The setting I am thinking of is that of a triangulated category with a model, but it would be interesting to have more general answers as well. A good reference would also be appreciated.</p> http://mathoverflow.net/questions/28435/automatically-extract-a-bibitem-not-bibtex-from-mathscinet Automatically extract a bibitem (not BibTeX!) from MathSciNet? Andreas Holmstrom 2010-06-16T21:38:20Z 2010-06-16T22:34:33Z <p>I am writing a small thing in which I am required to use manually formatted \bibitem entries rather than a BibTeX file. This takes a lot of time, and I probably get some of the formatting wrong. Is there a way of producing such entries automatically, for example from MathSciNet or from the BibTeX items created by MathSciNet? For arXiv preprints, there is a great tool from the Courant Research Centre (<a href="http://www.crcg.de/arXivToBibTeX/" rel="nofollow">here</a>) which can produce BibTeX as well as bibitem entries, and there should be something similar for MathSciNet.</p> http://mathoverflow.net/questions/20551/sources-for-bibtex-entries/20627#20627 Answer by Andreas Holmstrom for Sources for Bibtex entries Andreas Holmstrom 2010-04-07T13:40:12Z 2010-04-07T13:40:12Z <p>The Courant Centre has a <a href="http://www.crcg.de/arXivToBibTeX/" rel="nofollow">useful webpage</a> which produces nice BibTeX entries for arXiv preprints, if you input a paper ID or an author ID.</p> <p>Random fact: The <a href="http://www.math.uiuc.edu/K-theory/" rel="nofollow">K-theory archive</a> has a loooong BibTeX file on the K-theory literature available for download.</p> http://mathoverflow.net/questions/6834/kunneth-formula-for-motivic-cohomology/6865#6865 Answer by Andreas Holmstrom for Kunneth formula for motivic cohomology Andreas Holmstrom 2009-11-26T01:59:05Z 2009-11-26T01:59:05Z <p>Very briefly, I believe the following is true: Motivic cohomology does not satisfy a Kunneth formula on the level of cohomology groups, but it does satisfy a kind of Kunneth formula on the level of some suitable derived category of sheaves. This should hold true in general for any Bloch-Ogus cohomology theory, I think.</p> http://mathoverflow.net/questions/6125/what-is-a-cohomology-theory-seriously/6758#6758 Answer by Andreas Holmstrom for What is a cohomology theory (seriously)? Andreas Holmstrom 2009-11-25T03:00:05Z 2009-11-25T03:00:05Z <p>I promised to write a longer answer, but I simply don't have time this week - sorry. What I wanted to point our was that although the idea that "every flavor of cohomology ever considered is nothing but the study of connected components in the hom-spaces of some (oo,1)-topos" is one of the most amazing ideas ever (imho), it is still not clear (at least to me) exactly how this works in all cases, even for abelian sheaf cohomology. For example, most people seem to believe that the right (oo,1)-topos for cohomology theories in algebraic geometry should be given by A1 (or "motivic") homotopy theory, but there is nothing in the literature about representability of p-adic cohomology theories such as rigid cohomology. I believe this might be because there is some technical problem, but I am not sure. There are also other issues and examples which are not clear (to me!).</p> <p>The other thing I wanted to do was to clarify various pieces of terminology related to cohomology in algebraic geometry, for example, "generalized cohomology" means different things in different articles, and there are many different notions of "universal cohomology". Maybe I can expand on this later.</p> <p>One small remark: Motivic cohomology is usually thought of as the universal Bloch-Ogus cohomology, while the universal Weil cohomology should probably be pure motives with respect to rational equivalence ("probably", because it depends on what exactly you mean by "universal" and "Weil cohomology"). The two notions are closely related though.</p> <p>(Aside: The reason I am very busy this week is that I suddenly find myself writing job applications, after essentially solving my thesis problem last week, and one of the main reasons I could solve my thesis problem was that I applied Urs' unified point of view on cohomology in a new setting.) </p> http://mathoverflow.net/questions/1675/how-to-do-computations-using-the-decomposition-theorem-for-perverse-sheaves/6753#6753 Answer by Andreas Holmstrom for How to do Computations Using the Decomposition Theorem for Perverse Sheaves Andreas Holmstrom 2009-11-25T01:46:31Z 2009-11-25T01:46:31Z <p>There is a winter school on the decomposition theorem in Freiburg, Germany, 22-26 Feb 2010. <a href="http://home.mathematik.uni-freiburg.de/kebekus/FebSchool/" rel="nofollow">Link</a>.</p> http://mathoverflow.net/questions/5179/global-fibrations-of-simplicial-sheaves/5637#5637 Answer by Andreas Holmstrom for global fibrations of simplicial sheaves Andreas Holmstrom 2009-11-15T18:53:08Z 2009-11-15T18:53:08Z <p>For model structures on simplicial sheaves, there is a difference between the Joyal-Jardine approach and the Brown-Gersten approach. This is well explained in Voevodsky's preprint: <em>Homotopy theory of simplicial presheaves in completely decomposable topologies</em>, available <a href="http://front.math.ucdavis.edu/0805.4578" rel="nofollow">here</a>. Briefly, the Brown-Gersten approach does not work for arbitrary sites, but it works for a class of sites defined in Voevodsky's paper - this class includes Noetherian finite-dimensional spaces. When the B-G approach works, the resulting model structure has better finiteness properties than the Joyal-Jardine model structure, which on the other hand can be defined for simplicial (pre)sheaves on any site.</p> http://mathoverflow.net/questions/1428/examples-and-intuition-for-arithmetic-schemes Examples and intuition for arithmetic schemes Andreas Holmstrom 2009-10-20T13:47:52Z 2009-11-05T21:47:49Z <p>How should a beginner learn about arithmetic schemes (interpret this as you wish, or as a regular scheme, proper and flat over Spec(Z))? What are the most important examples of such schemes? Good references? What kind of intuition do people have for such schemes?</p> http://mathoverflow.net/questions/105575/finiteness-of-stable-homotopy-groups-of-spheres Comment by Andreas Holmstrom Andreas Holmstrom 2012-08-29T17:56:21Z 2012-08-29T17:56:21Z Thanks for all the comments and thanks to Peter May for an excellent answer! @Ryan: Sure, a proof is a proof, and Serre's work is amazing, but I still think it is meaningful to ask for conceptual reasons for believing something. Part of my motivation is that there are many unproven conjectures suggesting that this or that cohomological invariant should be finite (or finitely generated) and it would be interesting to hear the reasons (if any!) that experts believe such conjectures. http://mathoverflow.net/questions/61852/a-question-on-k-1-of-an-elliptic-curve/62120#62120 Comment by Andreas Holmstrom Andreas Holmstrom 2011-04-21T19:21:59Z 2011-04-21T19:21:59Z Thanks to both of you for the clarifications! To profilesdroxford5: It is possible that I in the future might want to use your construction (2) for an example in some paper, and if so I would like to give you due credit. If you prefer me to put your real name there, please just drop me an email. http://mathoverflow.net/questions/61852/a-question-on-k-1-of-an-elliptic-curve/62120#62120 Comment by Andreas Holmstrom Andreas Holmstrom 2011-04-19T15:15:19Z 2011-04-19T15:15:19Z Thanks, that is very helpful. However, although surely the cokernel you refer to is &quot;big&quot;, it could still in principle be a very big torsion group, right? To your comment (1), the answer is yes, but is it not equivalent? Is anything known about whether the groups $K'_0(\mathcal{E}_p)^{(1)}$ can contain a non-torsion element? http://mathoverflow.net/questions/61852/a-question-on-k-1-of-an-elliptic-curve Comment by Andreas Holmstrom Andreas Holmstrom 2011-04-16T21:59:12Z 2011-04-16T21:59:12Z Hej Daniel - bra fr&#229;ga, men sv&#229;rt att svara inom 600 tecken!! Vore f&#246;r &#246;vrigt kul att ses n&#229;n g&#229;ng, v&#229;ra intressen &#228;r ju inte alltf&#246;r olika. &#196;r i Uppsala ibland. http://mathoverflow.net/questions/36802/is-cosimplicialalgebras-left-proper Comment by Andreas Holmstrom Andreas Holmstrom 2010-08-26T22:04:05Z 2010-08-26T22:04:05Z Hi Urs, this may or may not be useful to you, but there is a proof of properness for a certain model structure on commutative monoids in symmetric spectra. See Hornbostel (arXiv:1005.4546, Thm 3.17), and the reference he gives to Shipley: A convenient model structure... (article available on her webpage). Maybe some idea used in this proof could also be useful in your setting. http://mathoverflow.net/questions/34801/dirichlets-regulator-vs-beilinsons-regulator Comment by Andreas Holmstrom Andreas Holmstrom 2010-08-07T15:05:30Z 2010-08-07T15:05:30Z Hi Robin, sure, both the Beilinson regulator and the Dirichlet regulator are defined on $K_1(O_F)$, but the former is defined in terms of Gillet's general theory of Chern classes, and the latter in terms of the explicit logarithm formula found in any algebraic number theory textbook, and the question is if both definitions agree, or if they differ by some constant factor. http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-27T19:24:02Z 2010-07-27T19:24:02Z Tom, I asked two new questions based on your reply, in the hope that more people will see the questions. I would still be very interested in what exactly was wrong and what was right in your original answer though. http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-27T00:33:57Z 2010-07-27T00:33:57Z Aha, I guess I never had to think of uncountable homotopy colimits so far ;-) and thanks, I will check the reference to May. http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-26T21:01:00Z 2010-07-26T21:01:00Z Actually I was not completely sure myself what I meant. I am trying to understand this for a specific application and wasn't sure which case I need. When writing the question I was thinking of a situation where the colimit happens to exist, but I also had in mind a homotopy colimit. Now I learnt from Tom that they coincide, which was a big surprise. About your last question: As far as I understand one can define sequential hocolim in any triangulated category, without assuming existence of a model, as a cone of the shift map on the direct sum of all terms, or something like that. http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang/33403#33403 Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-26T20:44:19Z 2010-07-26T20:44:19Z I am not sure what compactly generated actually means for a model category which is not stable (and in the latter case I interpret compactly generated as saying that the homotopy category is compactly generated as a triangulated category). Do you know of a more general definition? http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang/33403#33403 Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-26T18:36:12Z 2010-07-26T18:36:12Z That it an excellent answer. Do you have a reference for the statement that sequential colim equals hocolim in a compactly generated stable model category? Or is it easy to prove? Regarding triangulated categories not of the above form, I am quite sure they never occur in nature, but there are some artificial examples of Muro/Schwede/Strickland. http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang/33357#33357 Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-26T09:06:49Z 2010-07-26T09:06:49Z Maybe an argument in this spirit could work, but one question would be the following: Does homotopy colimits commute with homotopy colimits in general? http://mathoverflow.net/questions/33345/if-a-colimit-of-distinguished-triangles-exists-is-it-also-a-distinguished-triang/33357#33357 Comment by Andreas Holmstrom Andreas Holmstrom 2010-07-26T07:08:04Z 2010-07-26T07:08:04Z Yes, I'm interested in the motivic stable homotopy category over some base scheme. Most statements that hold in the topological setting should hold there as well. http://mathoverflow.net/questions/28435/automatically-extract-a-bibitem-not-bibtex-from-mathscinet/28439#28439 Comment by Andreas Holmstrom Andreas Holmstrom 2010-06-16T23:15:47Z 2010-06-16T23:15:47Z Hi Matthew, the bbl file was very useful. Thanks a lot, and hope all is well with you. (and thanks to Willie as well!) http://mathoverflow.net/questions/16354/does-anyone-have-an-electronic-copy-of-waldspurgers-sur-les-coefcients-de-four Comment by Andreas Holmstrom Andreas Holmstrom 2010-03-03T06:56:05Z 2010-03-03T06:56:05Z Have you tried asking Waldspurger himself for an electronic copy? His email address is here: <a href="http://people.math.jussieu.fr/~waldspur/" rel="nofollow">people.math.jussieu.fr/~waldspur</a>