Diophantine and cohomological dimensions

2013/05/23 by Daniel Krashen, Krashen, Daniel, Eliyahu Matzri +1
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1305.5295

9 pages, comments welcome

arxiv created 2013/05/23 · openalex publication_date 2013/05/23 · arxiv updated 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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