most recent 30 from http://mathoverflow.net 2013-05-21T23:22:33Z http://mathoverflow.net/feeds/user/12884 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110754/mixed-tate-motives THC 2012-10-26T14:11:28Z 2012-10-26T15:03:10Z

<p>Hi there, in recent times I was reading texts about motives, and I want to ask something about Tate motives which is not clear to me (as I came across different definitions in different texts).</p> <p>Let $V_k$ be the category of (projective) k-varieties. I read that the polynomial ring $\mathbb{Z}[\mathbb{L}] \subset K_0(V_k)$, the latter being the Grothendieck ring of $V_k$, with $\mathbb{L}$ the Lefschetz class $[\mathbb{A}_1]$, "corresponds to" mixed Tate motives generated by the Tate objects $\mathbb{Q}(m)$ in the Grothendieck ring $K_0(M_k)$, $M_k$ being the category of pure $k$-motives. In another article one rather spoke about the subring $\mathbb{Z}[\mathbb{L},\mathbb{L}^{-1}] \subset K_0(M_k)$ ($\mathbb{L}$ now the Lefschetz motive). And in yet another paper I read that mixed Tate motives are defined differently.</p> <p>My question is: is one of the two first approaches indeed the correct way to see mixed Tate motives ? Or is this a restricted way to define them ? </p> <p>I am especially interested in the connection between mixed Tate motives and $\mathbb{Z}$-varieties which are polynomial-countable. (When assuming the Tate conjecture, these varieties would have mixed Tate motives, and conversely.)</p> <p>Thanks !!! </p>

http://mathoverflow.net/questions/97099/what-is-the-lefschetz-principle-examples THC 2012-05-16T08:50:16Z 2012-05-16T18:21:45Z

<p>Hi there, can anyone explain to me what the "Lefschetz Principle" is by some clear "classical" examples (not relying explicitly on model theory, say). Thanks !</p>

http://mathoverflow.net/questions/96572/automorphism-groups-of-fields THC 2012-05-10T13:33:42Z 2012-05-10T13:33:42Z

<p>Hi there,</p> <p>is there a classification/characterization of fields <strong>K</strong> for which the automorphism group Aut(<strong>K</strong>) has the property that |Aut(<strong>K</strong>)| &lt; |<strong>K</strong>| (e.g. finite fields, the rationals and reals) ? What about the same question for real-closed fields <strong>K</strong> ? Many thanks ...</p>

http://mathoverflow.net/questions/86446/ihara-zeta-function THC 2012-01-23T13:51:45Z 2012-01-23T14:15:56Z

<p>Is there a natural connection between the Ihara zeta function of a graph, and (for instance) the Riemann zeta function of certain varieties over finite fields ? Thanks.</p>

http://mathoverflow.net/questions/85797/automorphism-group-of-a-scheme-2 THC 2012-01-16T11:11:28Z 2012-01-16T12:19:08Z

<p>Hi,</p> <p>I have the following two questions about automorphism groups of schemes. First of all, let $S$ be a scheme, and $S^c$ its set of closed points. What is the connection between $Aut(S)$ and $Aut(S^c)$ ? Secondly, let $S$ be a $\mathbb{Z}$-scheme, and $S_k$ the base-extension to some field k. What is the precise relation between their automorphism groups ? Thanks,</p> <pre><code>THC </code></pre>

http://mathoverflow.net/questions/81903/something-diophantine THC 2011-11-25T16:32:29Z 2011-11-25T16:32:29Z

<p>Hi there, recently I came across the following divisibility question, and I wondered if much can be said about it. Let $p$ and $q$ be different primes, and suppose $p^n + q^r$ divides $p^{2m} - 1$, where $n$, $m$, $r$ are positive integers, $n$ divides $m$, and $q^r > p^m$. Is a classification of the triples $(n,m,r)$ within reach ? Thanks !</p>

http://mathoverflow.net/questions/57106/group-scheme-of-infinite-dimensional-linear-groups THC 2011-03-02T11:39:01Z 2011-03-02T12:59:30Z

<p>Hi there, I know there are fairly straightforward ways to write down the schemes of infinite dimensional projective spaces (not restricting myself to only countable dimensions), but what happens with infinite dimensional <em>general linear groups</em> ? Is there a well-known, standard way to define its group scheme, just as in the finite dimensional case ? Or is this usually done using Ind-scheme constructions ? (And if so, can somebody describe it in a nutshell for, e.g., uncountable dimensions ?)</p> <p>Thanks !!</p>

http://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme THC 2011-02-10T15:28:11Z 2011-02-20T10:50:11Z

<p>Hi there,</p> <p>I have a probably stupid question on schemes ... Let S be a scheme, and let A be its automorphism group. Does A carry a scheme structure itself, that is, can one see A as a group scheme ? Thanks !</p>

http://mathoverflow.net/questions/110754/mixed-tate-motives/110761#110761 THC 2012-10-30T10:23:36Z 2012-10-30T10:23:36Z

@unknown (google): Could you be a little more precise about what you mean here with &quot;at the K-group level&quot; ?

http://mathoverflow.net/questions/97099/what-is-the-lefschetz-principle-examples THC 2012-05-16T13:48:47Z 2012-05-16T13:48:47Z

I corrected the question, and hope it is better now. As I misread the term, thinking it was &quot;Lipschitz&quot;, google did not give much :-)

http://mathoverflow.net/questions/97099/what-is-the-lefschetz-principle-examples/97102#97102 THC 2012-05-16T13:47:04Z 2012-05-16T13:47:04Z

You are right - I misread the term in a paper - this is corrected now. Thanks !

http://mathoverflow.net/questions/96572/automorphism-groups-of-fields THC 2012-05-10T15:25:20Z 2012-05-10T15:25:20Z

General field automorphisms. And indeed, |.| = cardinality.

http://mathoverflow.net/questions/86446/ihara-zeta-function/86449#86449 THC 2012-01-25T08:21:02Z 2012-01-25T08:21:02Z

Ah, thanks. Are there other zeta functions for graphs which relate more directly to the Riemann zeta of varieties over finite fields ?

http://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme/56054#56054 THC 2011-02-21T12:46:43Z 2011-02-21T12:46:43Z

Dear Sandor, very informative ! Can you say a word about &quot;and hence it inherits a natural scheme structure&quot; ? (Why this is when dealing with a subgroup quotient ?) I think the finiteness outcome is not an obstruction for me, since eventually my automorphism schemes will look like Chevalley group schemes ...

http://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme/55049#55049 THC 2011-02-15T15:26:48Z 2011-02-15T15:26:48Z

I guess that in general, one cannot show that any automorphism extends to one of the ambient projective space, but the class that I am interested in has this property :-)

http://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme/55049#55049 THC 2011-02-15T15:23:44Z 2011-02-15T15:23:44Z

Hi, Dan - yep, I knew (it's only &quot;a for instance sentence&quot;) :-)

http://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme/55049#55049 THC 2011-02-15T09:28:07Z 2011-02-15T09:28:07Z

Thanks ! Is there a &quot;direct&quot; way to do it for flat and projective schemes, that is, without using the Hilbert scheme ? (For instance when one works with base a field.)