When is Galois cohomology free or trivial?
| dc.creator | Lemire, Nicole | |
| dc.creator | Minac, Jan | |
| dc.creator | Swallow, John | |
| dc.date | 2004-10-29 | |
| dc.date | 2005-03-01 | |
| dc.date.accessioned | 2026-07-07T06:21:07Z | |
| dc.date.available | 2026-07-07T06:21:07Z | |
| dc.description | Let 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.description | 29 pages; removed hypothesis on perfect fields in main results, and added references | |
| dc.identifier | https://arxiv.org/abs/math/0410617 | |
| dc.identifier | http://arxiv.org/abs/math/0410617 | |
| dc.identifier | New York J. Math. 11 (2005), 291--302 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95502 | |
| dc.subject | Number Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 12G05; 19D45 | |
| dc.title | When is Galois cohomology free or trivial? | |
| dc.type | text |