Quicklists
Javascript must be enabled

John Swallow : Galois module structure of Galois cohomology

root

123 Views

NOTE SEMINAR TIME: NOON!! Abstract: Let p be a prime number, F a field containing a primitive pth root of unity, and E/F a cyclic extension of degree p, with Galois group G. Let G_E be the absolute Galois group of E. The cohomology groups H^i(E,Fp)=Hî(G_E,Fp) possess a natural structure as FpG-modules and decompose into direct sums of indecomposables. In the 1960s Boreviè and Faddeev gave decompositions of E^*/E^*p -- the case i=1 -- for local fields. We describe the case i=1 for arbitrary fields, and then, using the Bloch-Kato Conjecture, we also determine the case i>1. No small surprise arises from the fact that there exist indecomposable FpG-modules which never appear in these module decompositions. We give several consequences of these results, notably a generalization of the Schreier formula for G_E, connections with Demu¹kin groups, and new families of pro-p-groups that cannot be realized as absolute Galois groups. These results have been obtained in collaboration with D. Benson, J. Labute, N. Lemire, and J. Mináè.

Please select playlist name from following

Report Video

Please select the category that most closely reflects your concern about the video, so that we can review it and determine whether it violates our Community Guidelines or isn’t appropriate for all viewers. Abusing this feature is also a violation of the Community Guidelines, so don’t do it.

0 Comments

Comments Disabled For This Video