Timeline for Borel's presentation for the cohomology of a Flag Variety
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2019 at 20:31 | vote | accept | DCT | ||
| Mar 8, 2019 at 13:57 | comment | added | Jason Starr | The answer by @VictorPetrov completely settles the question. I am leaving my answer in case it helps to see how to prove some of these results using the Leray spectral sequence. | |
| Mar 8, 2019 at 12:41 | answer | added | Victor Petrov | timeline score: 9 | |
| Mar 7, 2019 at 16:01 | comment | added | Jason Starr | The reference in Fulton is Example 1.9.1, p. 23. | |
| Mar 7, 2019 at 15:34 | comment | added | Jason Starr | Regarding Chow $A^*$, for every semisimple group $G$, the Bruhat decomposition is an "affine space cell decomposition" of $G/B$. Thus, the cycle class map $A^*(G/B)\to H^*(G/B;\mathbb{Z})$ is an isomorphism (there is a reference for this in Chapter 1 of Fulton's Intersection theory). | |
| Mar 7, 2019 at 14:47 | answer | added | Nicholas Kuhn | timeline score: 9 | |
| Mar 7, 2019 at 14:41 | answer | added | Jason Starr | timeline score: 6 | |
| Mar 7, 2019 at 11:52 | comment | added | Jason Starr | I just realized that you are not asking about the positive characteristic of the ground field, but about the positive characteristic of the field of coefficients for your cohomology theory. My comment above does not address that. | |
| Mar 7, 2019 at 11:32 | comment | added | Jason Starr | For split $(G,B,T)$ of a given type, additively the cohomology of $G/B$ is the same in characteristic $0$ or in characteristic $p$, since the Bruhat decomposition is an "affine paving" and the combinatorics of the affine space "cells" are independent of the characteristic. Since intersection numbers are also constant for flat, proper morphisms, I guess this also implies that the ring structure is also "constant" in specializing from characteristic $0$ to characterisic $p$: use intersection numbers to prove injectivity of $K[T^\vee]/(K[T^\vee]^W_+)\to H^*(G/B,K)$. | |
| Mar 7, 2019 at 3:51 | history | edited | DCT | CC BY-SA 4.0 |
added 20 characters in body
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| Mar 7, 2019 at 3:40 | history | asked | DCT | CC BY-SA 4.0 |