Timeline for Structure theorem for finitely generated Z[G] modules
Current License: CC BY-SA 2.5
4 events
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| Nov 11, 2010 at 18:58 | comment | added | Emerton | This has some analogy with the situation in number theory: in number theory, we have Hecke correspondences acting on certain algebraic varieties (Shimura varieties), and we form the Hecke algebra generated by all these correspondences, which as a $\mathbb Z$-module is free of finite rank (just like your $\mathbb Z[G]$), and then we consider the action of this Hecke algebra on the cohomology of the variety, and use techniques of the kind described in my answer to get some handle on the possible module structure that results. | |
| Nov 11, 2010 at 17:58 | vote | accept | B. Naskrecki | ||
| Nov 11, 2010 at 17:58 | comment | added | B. Naskrecki | The question came from topology and group actions of abelian group $G$ acting on a product of spheres. We then consider action of group ring $\mathbb{Z}[G]$ on singular cohomology modules. | |
| Nov 11, 2010 at 3:50 | history | answered | Emerton | CC BY-SA 2.5 |