Timeline for How to fit res map into a long exact sequence?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| May 25, 2010 at 18:54 | comment | added | Emerton | The standard technique for computing $H^n(G,A)$ when $n = 0$ is just the definition: one looks for $G$-fixed elements in $A$. For $n = 1$, here is a common method: the $G$-action on $A$ gives a homo. $G \to Aut(A)$; let $H$ be the kernel. (So $H$-acts trivially on $A$.) Then one has the inflation-restriction sequence $0 \to H^1(G/H,A) \to H^1(G,A) \to Hom_{G/H}(H^{ab},A)$ (where the last term is written as $Hom$ rather than $H^1$ precisely because $H$ acts trivially on $A$). Now one hopes that the outer two terms are easier to compute, and can be pieced together to understand $H^1(G,A)$. | |
| May 25, 2010 at 4:04 | answer | added | Torsten Ekedahl | timeline score: 2 | |
| May 25, 2010 at 3:33 | answer | added | Cam McLeman | timeline score: 2 | |
| May 25, 2010 at 3:27 | history | asked | user1832 | CC BY-SA 2.5 |