Timeline for What is the possible usefulness of étale topology and cohomology apart from the resolution of the Weil conjecture ?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2012 at 13:50 | comment | added | Minhyong Kim | Oh well. Here imrn.oxfordjournals.org/content/2002/28/1505.short is a trivial bit of self-promotion, since you did ask about manifold topology. | |
| Mar 29, 2012 at 12:54 | answer | added | Alexander Chervov | timeline score: 2 | |
| Mar 29, 2012 at 3:30 | answer | added | Alex B. | timeline score: 7 | |
| Mar 29, 2012 at 3:12 | answer | added | user22479 | timeline score: 11 | |
| Mar 28, 2012 at 23:21 | comment | added | christian | Thank you for the link. I should have checked it before posting the question. | |
| Mar 28, 2012 at 1:33 | comment | added | Hunter Brooks | Many interesting answers here: mathoverflow.net/questions/6070/etale-cohomology-why-study-it | |
| Mar 28, 2012 at 1:21 | answer | added | Felipe Voloch | timeline score: 6 | |
| Mar 28, 2012 at 0:54 | answer | added | anonymous | timeline score: 3 | |
| Mar 27, 2012 at 22:41 | comment | added | Jim Humphreys | I edited the English a bit. More important, this is a very broad inquiry which allows for multiple possible answers even in the specific areas you mention. In a more algebraic direction, etale cohomology has been an essential tool in the character theory of finite groups of Lie type as pioneered by Deligne and Lusztig in the mid-1970s and exposed in several books as well as many research papers. The subject is definitely useful beyond the Weil conjectures. | |
| Mar 27, 2012 at 22:39 | comment | added | Daniel Loughran | As for explicit uses outside the Weil conjectures, étale cohomology groups come equipped with an action of the absolute galois group of the field in question, and hence give rise to naturally occuring Galois representations which are of great interest to number theorists | |
| Mar 27, 2012 at 22:39 | comment | added | Daniel Loughran | In complex geometry you have the usual de Ram and Betti cohomology groups and the analytic topology, so in some respects you don't really "need" étale cohomology. For me, the whole point of étale cohomology is that it exists over general fields (e.g. finite fields). | |
| Mar 27, 2012 at 22:38 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
edited body; edited title
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| Mar 27, 2012 at 20:06 | history | asked | christian | CC BY-SA 3.0 |