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Hilbert 90 for Galois cohomology

Nicole Lemire·Jan Minac·Andrew Schultz·John Swallow
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Abstract

Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n.

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Nicole Lemire, Jan Minac, Andrew Schultz, John Swallow. 2006-01-27. Hilbert 90 for Galois cohomology. https://arxiv.org/abs/math/0601663

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