Galois module structure of Galois cohomology and partial Euler-Poincare characteristics

dc.creatorLemire, Nicole
dc.creatorMinac, Jan
dc.creatorSwallow, John
dc.date2004-09-24
dc.date2006-10-20
dc.date.accessioned2026-07-07T09:46:43Z
dc.date.available2026-07-07T09:46:43Z
dc.descriptionLet 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.description30 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.identifierhttps://arxiv.org/abs/math/0409484
dc.identifierhttp://arxiv.org/abs/math/0409484
dc.identifierJ. Reine Angew. Math. 613 (2007), 147--173
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163626
dc.subjectNumber Theory
dc.subjectK-Theory and Homology
dc.subject12G05; 19D45
dc.titleGalois module structure of Galois cohomology and partial Euler-Poincare characteristics
dc.typetext

Files

Collections