Timeline for Examples for Decomposition Theorem
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2010 at 17:40 | history | edited | Mike Skirvin | CC BY-SA 2.5 |
Corrected mistakes pointed out by Geordie Williamson in the comments.
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| Mar 6, 2010 at 17:35 | comment | added | Mike Skirvin | Thanks for pointing out that first embarrassing mistake. Thankfully the subsequent discussion is unharmed, as far as I know. As for geometric Satake, I guess I remember Ginzburg using the decomposition theorem when defining convolution. I didn't realize that this was a simpler fact. | |
| Mar 6, 2010 at 11:09 | comment | added | Geordie Williamson | One should probably point out that the the first stated "Fact" is not true. This is only true for the direct image of the constant sheaf. A stupid example: take the map to A_2, given by blowing up the origin. The push-forward of the constant sheaf on the exceptional divisor shifted by 1 is not perverse. Also, the decomposition theorem is not needed in the proof of the geometric Satake isomorphism. (MV use modular coefficients, for which the decomposition theorem doesn't hold in general.) The reason that convolution preserves perverse sheaves is simpler (see MV's paper). | |
| Nov 25, 2009 at 22:30 | comment | added | Mike Skirvin | Your edit looks better than the original post, so I don't mind at all. And feel free to edit further in the future. I know my answer could have been written more nicely and included quite a few more details, but I ran out of time and energy when I first wrote it. | |
| Nov 25, 2009 at 21:17 | comment | added | Ilya Nikokoshev | I hope you don't mind I edited your answer! There's a "revert" link if you don't like it. I plan to rewrite some parts a bit more as I understand them better, is it ok? | |
| Nov 25, 2009 at 21:16 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
linkify, formatting, headers, some minor changes
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| Nov 25, 2009 at 20:52 | comment | added | Ilya Nikokoshev | Though the examples are less elementary than I hoped (and I had general knowledge of both), they are indeed deep and you explained the Spring theory very clear way. Thanks for the answer! | |
| Nov 25, 2009 at 20:48 | vote | accept | Ilya Nikokoshev | ||
| Nov 25, 2009 at 20:48 | history | bounty ended | Ilya Nikokoshev | ||
| Nov 23, 2009 at 20:41 | history | edited | Mike Skirvin | CC BY-SA 2.5 |
added 1835 characters in body
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| Nov 23, 2009 at 18:12 | comment | added | Gil Kalai | To what extent does Lusztig's work rely on the decomposition theorem? | |
| Nov 19, 2009 at 19:12 | history | answered | Mike Skirvin | CC BY-SA 2.5 |