Diophantine and cohomological dimensions

Krashen, Daniel; Matzri, Eliyahu

doi:10.1090/S0002-9939-2015-12461-6

Diophantine and cohomological dimensions
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by Daniel Krashen and Eliyahu Matzri PDF

Proc. Amer. Math. Soc. 143 (2015), 2779-2788 Request permission

Abstract:

We give explicit linear bounds on the $p$-cohomological dimension of a field in terms of its Diophantine dimension. In particular, we show that for a field of Diophantine dimension at most $4$, the $3$-cohomological dimension is less than or equal to the Diophantine dimension.

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