Galois module structure of Galois cohomology and partial Euler-Poincare characteristics
| dc.creator | Lemire, Nicole | |
| dc.creator | Minac, Jan | |
| dc.creator | Swallow, John | |
| dc.date | 2004-09-24 | |
| dc.date | 2006-10-20 | |
| dc.date.accessioned | 2026-07-07T09:46:43Z | |
| dc.date.available | 2026-07-07T09:46:43Z | |
| dc.description | Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group G_F of F. Using the Bloch-Kato Conjecture we determine the structure of the cohomology group H^n(U,Fp) as an Fp[G_F/U]-module for all n in N. Previously this structure was known only for n=1, and until recently the structure even of H^1(U,Fp) was determined only for F a local field, a case settled by Borevic and Faddeev in the 1960s. We apply these results to study partial Euler-Poincare characteristics of open subgroups N of the maximal pro-p quotient T of G_F. We extend the notion of a partial Euler-Poincare characteristic to this case and we show that the nth partial Euler-Poincare characteristic Theta_n(N) is determined only by Theta_n(T) and the conorm in H^n(T,Fp). | |
| dc.description | 30 pages; implemented minor changes suggested by the referee; strengthened Proposition 3 in section 7; now considers partial Euler-Poincare characteristics only in the case when the Galois group of the maximal p-extension of the field F is finitely generated | |
| dc.identifier | https://arxiv.org/abs/math/0409484 | |
| dc.identifier | http://arxiv.org/abs/math/0409484 | |
| dc.identifier | J. Reine Angew. Math. 613 (2007), 147--173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163626 | |
| dc.subject | Number Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 12G05; 19D45 | |
| dc.title | Galois module structure of Galois cohomology and partial Euler-Poincare characteristics | |
| dc.type | text |