When is Galois cohomology free or trivial?

Details When is Galois cohomology free or trivial? When is Galois cohomology free or trivial?

2004-10-29

arxiv.org/abs/math/0410617v2

New York J. Math. 11 (2005), 291--302

Mathematics

Number Theory

29 pages; removed hypothesis on perfect fields in main results, and added references

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

When is Galois cohomology free or trivial? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with When is Galois cohomology free or trivial?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and When is Galois cohomology free or trivial? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479944