When is Galois cohomology free or trivial?
نویسندگان
چکیده
Let p be a prime, F a field containing a primitive pth root of unity, and E/F a cyclic extension of degree p. Using the Bloch–Kato Conjecture we determine precise conditions for the cohomology group Hn(E) := H(GE ,Fp) to be free or trivial as an Fp[Gal(E/F )]-module, and we examine when these properties for Hn(E) are inherited by Hk(E), k > n. By analogy with cohomological dimension, we introduce notions of cohomological freeness and cohomological triviality, and we give examples of Hn(E) free or trivial for each n ∈ N with prescribed cohomological dimension.
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