Timeline for Compute corestriction map on group cohomology in Magma
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9 at 14:29 | answer | added | Kasper Andersen | timeline score: 3 | |
| Nov 7 at 9:25 | comment | added | Jef | @KasperAndersen: I don't think this is the problem, I can evaluate z([H.1,H.1]) for example. If I put in f(<G.1,G.1>) I get the same error. | |
| Nov 6 at 22:12 | comment | added | Kasper Andersen | I think the first error is due to wrong syntax, the command should be f(<G.1,G.1>) and not f([G.1,G.1]). | |
| Nov 6 at 19:28 | answer | added | Mikhail Borovoi | timeline score: 2 | |
| Nov 6 at 17:39 | comment | added | Mikhail Borovoi | Right action: Right! I will post a right-action version a bit later. | |
| Nov 6 at 17:36 | comment | added | Mikhail Borovoi | This is an inhomogeneous version of the formula for ${\rm cor}^n$ for all $n\ge 0$ in Section 3.6 of this preprint. This inhomogeneous formula will soon appear in the next version of this preprint in Appendix E. | |
| Nov 6 at 17:26 | comment | added | Jef | @MikhailBorovoi Thanks for your comments, they are very helpful. Do you have a reference for this formula? One subtle feature is that Magma views $G$-modules as acting on the right (as opposed to the traditional action on the left), so this might affect the formula. | |
| Nov 6 at 17:15 | comment | added | Mikhail Borovoi | Set $X=H\backslash G$. I think that in your example $X=M\smallsetminus \{0\}$. Choose a section $$ s\colon X\to G$$ of the natural projection $G\to X=H\backslash G$. Let $c\colon H\times H\to M$ be a 2-cochain for $H$. Then the value of ${\rm cor}^2(c)$ on $(g_1,g_2)\in G\times G$ is $$\sum_{x\in X} s(x)\cdot c\big(\,s(x) g_1 s(xg_1)^{-1},\, s(xg_1) g_2 s(x g_1 g_2)^{-1}\,\big).$$ | |
| Nov 6 at 17:15 | comment | added | Mikhail Borovoi | I am not good with Magma functionalities, but I know an explicit formula for the corestriction map $${\rm cor}^2\colon C^2(H,M) \to C^2(G,M)$$ that you can easily implement in Magma. | |
| Nov 6 at 15:43 | history | asked | Jef | CC BY-SA 4.0 |