Timeline for Cohomology of finite $p$-groups over integers in local fields
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2021 at 21:56 | vote | accept | frafour | ||
| Mar 3, 2021 at 20:27 | comment | added | user42024 | @frafour Yep that's right $\sigma$ is the action of a chosen generator and $1=\mathrm{id}$ is the identity map. I am not sure about the precise reference (probably anything on Tate cohomology) but this just follows from the fact that the analogous complex $\ldots \xrightarrow{1+\sigma +\ldots } \mathbb Z[G] \xrightarrow{\sigma - \mathrm{id}} \mathbb Z[G]$ is a free resolution of trivial module $\mathbb Z$ as a $\mathbb Z[G]$-module (plus the formula $H^i(G,M)=\mathrm{Ext}^i_{\mathbb Z[G]}(\mathbb Z,M)$). | |
| Mar 3, 2021 at 17:05 | comment | added | frafour | Thank you very much for the answer! To be sure: $\sigma$ is the automorphism given by the action of the generator of $G$? And $1$ is the identity map? Also could you give a reference for the first statement, the fact that cohomology is computed by this resolution? | |
| Mar 2, 2021 at 20:48 | history | answered | user42024 | CC BY-SA 4.0 |