When is Galois cohomology free or trivial?

dc.creatorLemire, Nicole
dc.creatorMinac, Jan
dc.creatorSwallow, John
dc.date2004-10-29
dc.date2005-03-01
dc.date.accessioned2026-07-07T06:21:07Z
dc.date.available2026-07-07T06:21:07Z
dc.descriptionLet p be a prime and F a field containing a primitive pth root of unity. Let E/F be a cyclic extension of degree p and G_E < G_F the associated absolute Galois groups. We determine precise conditions for the cohomology group H^n(E)=H^n(G_E,Fp) to be free or trivial as an Fp[Gal(E/F)]-module. We examine when these properties for H^n(E) are inherited by H^k(E), k>n, and, by analogy with cohomological dimension, we introduce notions of cohomological freeness and cohomological triviality. We give examples of H^n(E) free or trivial for each n in N with prescribed cohomological dimension.
dc.description29 pages; removed hypothesis on perfect fields in main results, and added references
dc.identifierhttps://arxiv.org/abs/math/0410617
dc.identifierhttp://arxiv.org/abs/math/0410617
dc.identifierNew York J. Math. 11 (2005), 291--302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95502
dc.subjectNumber Theory
dc.subjectK-Theory and Homology
dc.subject12G05; 19D45
dc.titleWhen is Galois cohomology free or trivial?
dc.typetext

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