Timeline for Sheaf description of $G$-bundles
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2019 at 8:52 | comment | added | ACL | @LSpice, it is at the beginning of section III (Interlude: Review of algebraic groups), page 211. The statement of Chevalley's theorem is on page 212. The key word is “construction”. (I imagine it shortens the expression “construction tensorielle”.) | |
| Dec 1, 2019 at 3:05 | comment | added | LSpice | @ACL, do you happen to remember where in Katz - A conjecture in the arithmetic theory of differential equations that result appears? The word 'tensor' appears 4 times in the paper, and none of them seems obviously to be the quoted result. | |
| S May 4, 2016 at 15:47 | history | suggested | Armando j18eos | CC BY-SA 3.0 |
I had correct the code!
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| May 4, 2016 at 15:37 | review | Suggested edits | |||
| S May 4, 2016 at 15:47 | |||||
| Jan 31, 2014 at 9:19 | comment | added | ACL | @AntonGeraschenko: I learnt this in Katz's paper on (Bulletin SMF, 1982, numdam.org/item?id=BSMF_1982__110__203_0). He refers to Chevalley's 1968 book on Lie groups. | |
| Jan 30, 2014 at 23:14 | comment | added | Anton Geraschenko | @ACL: Can you give me a reference for that? At some point I tried describing what sorts of tensor relations give a vector space the structure of a representation of given a finite group, but I didn't get anything I was happy with. I didn't know that there was a general result along these lines for affine algebraic groups. | |
| Jan 30, 2014 at 7:44 | comment | added | ACL | @Anton: Algebraic subgroups of $GL(n)$ can be described by matrices fixing some tensor; consequently, $G$-bundles can be described as a vector bundle + some tensors. | |
| Jan 30, 2014 at 4:56 | history | edited | Anton Geraschenko | CC BY-SA 3.0 |
Correction: Aut(F) should have been Isom(O^n, F). While I'm here, texifying and cleaning up a couple of stylistic things.
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| Oct 25, 2009 at 16:00 | comment | added | Charles Siegel | This is the closest to the sort of thing I was looking for. Since asking, I realized that there was an obvious description that was what I was looking for, for any fiber bundle with fiber F, a locally trivial F-bundle should be (it's in my scratch notebook, not fully proved but should work) equivalent to a sheaf of sets locally isomorphic to sheaf Hom(X,F). This recovers the equivalence for vector bundles, and does about what I want for G-bundles. | |
| Oct 25, 2009 at 15:59 | vote | accept | Charles Siegel | ||
| Oct 25, 2009 at 4:37 | history | edited | Anton Geraschenko | CC BY-SA 2.5 |
added 342 characters in body
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| Oct 25, 2009 at 4:01 | history | answered | Anton Geraschenko | CC BY-SA 2.5 |