Mikhail Bondarko
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Registered User
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I am a professor in St. Petersburg State University. I have several papers on (additive Galois module structure of) local fields, formal groups, and finite group schemes. Currently I am studying Voevodsky's motives and their cohomology. In the process I introduced the notion of a weight structure for a triangulated category; this seems to be an interesting piece of homological algebra (that possibly could be applied to algebraic topology). See http://arxiv.org/abs/0903.0091 for a survey of some of my recent results.
You can send me letters to mbondarko gmail.com. In particular, if you answered one of my questions, please tell me how can I mention you in my papers!
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Apr 23 |
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Repeated Homotopy Category of Chain Complexes I do not think that considering complexes over $K(C)$ is a good idea; I never met any mention of those. |
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Apr 18 |
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Decomposition of Motives of cellular varieties This argument works in any additive category where we have a similar formula. One can also consider Voevodsky's motives with rational coefficients, or Voevodsky-Suslin finite correspondences with rational coefficients modulo homotopy equivalence here. |
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Apr 12 |
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semicontinuity results for weights For weights a-la BBD there is an equality for any proper $f$ (since $f_*=f_!$); see Stabilities 5.1.14. |
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Apr 12 |
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What is the purpose of section 3 of BBD? I know that the filtered derived category was used in succeeding papers. Yet I was not able to understand whether it was used in BBD. |
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Apr 12 |
awarded | ● Nice Question |
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Apr 11 |
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What is the purpose of section 3 of BBD? Upd. added. |
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Apr 11 |
asked | What is the purpose of section 3 of BBD? |
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Apr 8 |
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How would you say that a small category is embedded into functors from a large $C'$ to abelian groups? Yes, this is quite correct! The category of $R$-modules is quite actual for me; yet I don't want to fix this setting. My problem is: I have a theorem that expresses $C'$ in terms of $C$, and I would also like to express $C$ in terms of functors that its objects induce on $C'$. Yet there are 'too many' functors from $C'$! |
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Apr 8 |
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How would you say that a small category is embedded into functors from a large $C'$ to abelian groups? Thank you! Sorry; I only just recollected that my $C'$ is isomorphic to the category of all additive functors from $C$ to abelian groups. So, the objects that come from an embedding of $C$ into $C'$ do yield compact generators. Yet are $k$-directed colimits suffice to obtain $C'$ from $C$? This is probably wrong for any $k$. |
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Apr 8 |
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How would you say that a small category is embedded into functors from a large $C'$ to abelian groups? I don't have any reasonable small subcategory inside $C'$. I also recollected that my $C$ does not canonically map into $C'$; I only have a bifunctor $C\times C'\to Ab$. |
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Apr 8 |
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How would you say that a small category is embedded into functors from a large $C'$ to abelian groups? I recalled that my small $C$ is not inside $C'$; I only have a bifunctor defined on $C\times C'$. |
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Apr 8 |
asked | How would you say that a small category is embedded into functors from a large $C'$ to abelian groups? |
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Apr 6 |
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Singularity locus in terms of ideals. I would also like to know other possibilities. |
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Apr 6 |
asked | Singularity locus in terms of ideals. |
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Mar 25 |
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When $R/(f)$ is regular? Upd. 2 added |
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Mar 25 |
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When $R/(f)$ is regular? deleted 82 characters in body |
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Mar 25 |
awarded | ● Nice Question |
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Mar 25 |
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When $R/(f)$ is regular? Upd. 2 added |
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Mar 25 |
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When $R/(f)$ is regular? Upd. added. |
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Mar 24 |
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When $R/(f)$ is regular? Yes, but how can I find the regular locus (or some open subscheme in it)? |
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Mar 24 |
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When $R/(f)$ is regular? Thank you! Yet I would like to have a finite number of conditions. |
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Mar 24 |
asked | When $R/(f)$ is regular? |
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Mar 16 |
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Regular subscheme of a projective limit of schemes Thank you!! It seems that I know how to reduce the general case to the local one. |
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Mar 12 |
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Non-uniqueness of smooth compactification So, smooth compactifications are certainly not unique; yet this non-uniqueness can be controlled to a certain extent. |
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Mar 12 |
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Non-uniqueness of smooth compactification A remark: though $U$ doesnotdetermine $Y$, for any cohomology theory that factorizes through Voevodsky′s motives the image $H(Y)\to H(U)$ is canonical and functorial (this is the zeroth level of the weight filtration). One can also look at weight complexes. In characteristic $p$ one can prove a somewhat similar result for any cohomology whose target is a $Z[1/p]$-linear category. |
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Mar 11 |
asked | Regular subscheme of a projective limit of schemes |
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Mar 6 |
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Which schemes can be presented as limits of smooth varieties? I'm sorry! I need the connecting morphisms to be dominant, but I forgot to write about this. |
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Mar 6 |
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Which schemes can be presented as limits of smooth varieties? I forgot to tell that I need the connecting morphisms to be dominant. |
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Mar 6 |
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Which schemes can be presented as limits of smooth varieties? Thank you! Are you sure that the connecting morphisms are dominant? Also, do you think that anything is known in the non-affine case? |
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Mar 6 |
asked | Which schemes can be presented as limits of smooth varieties? |
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Feb 26 |
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Does the Čech cohomology always yield long exact sequences from short ones? Cech cohomology yields a 'nice' cohomology theory if all the (multiple) intersections of the components of your covering have trivial cohomology (this is also true if you consider a limit of coverings). If you have a weird topological space, then you cannot achieve this condition; then you need hypercoverings. |
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Feb 23 |
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How would you call a subscheme of a smooth $S$-scheme? Upd. added. |
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Feb 23 |
asked | How would you call a subscheme of a smooth $S$-scheme? |
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Feb 21 |
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If $X,Y$ are regular and of finite type over $S$, can $X\times _S Y$ be embedded into a regular $S$-scheme? added 109 characters in body |
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Feb 21 |
asked | If $X,Y$ are regular and of finite type over $S$, can $X\times _S Y$ be embedded into a regular $S$-scheme? |
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Feb 20 |
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Realization of Voevodsky Motives over a perfect field in mixed categories. In order to apply the statement I cited you will also need a description of $M_{gm}(X)$ given by Cisinski and Deglise and Verdier duality. |
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Feb 20 |
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Realization of Voevodsky Motives over a perfect field in mixed categories. See Proposition 2.1.1, assertion 14 (and 2) of my preprint arxiv.org/abs/1105.0420 (page 19), its proof, and the papers cited. |
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Feb 17 |
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Motivic cohomology and cohomology of Milnor K-theory sheaf No, there is no such isomorphism in general. The problem is that Milnor K-groups just yield the $s$-th (co)homology of the complex of sheaves $Z(s)$. Probably, there is a comparison morphism (that is an isomorphism when $X$ is local); I have to think about the details here. |
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Feb 17 |
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Applications for intersection (co)homology and for the Decomposition Theorem for students? I assume that all the participants of the seminar know something about cohomology. On the other hand, they probably do not know why intersection (co)homology is useful. |
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Feb 16 |
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Applications for intersection (co)homology and for the Decomposition Theorem for students? Well, there are distinct students at our seminar; yet most of them never studied really advanced mathematics. |
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Feb 16 |
asked | Applications for intersection (co)homology and for the Decomposition Theorem for students? |
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Feb 8 |
awarded | ● Fanatic |
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Feb 3 |
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Another stupid question on l-adic sheaves: does a generically zero constructible sheaf vanish on an open subvariety? Thank you!!!!!! |
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Feb 3 |
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Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? Thank you, ulrich!!!! |
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Feb 2 |
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Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? Upd. added.; added 26 characters in body |
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Feb 2 |
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Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? Dear ulrich: is the corresponding Galois representation necessarily indecomposable? |
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Feb 2 |
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Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? Dear Donu: the Tate conjecture certainly yields that a direct summand of a motivic representation is motivic. Yet why can you prove anything about arbitrary subrepresentations? |
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Feb 1 |
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Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? Why does the semi-simplicity of motives imply the semi-simplicity of the corresponding representations? Representations could have subobjects that are not 'motivic'. |
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Feb 1 |
asked | Should the etale cohomology of a smooth projective variety (over rationals) be semi-simple; why? |
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Jan 28 |
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A canonical way to kill a subset of cohomology in a dg-algebra: via $A_\infty$-algebras? References? added 212 characters in body |
