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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
References
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Additional Information
  • Daniel Krashen
  • Affiliation: Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, Georgia
  • MR Author ID: 728218
  • ORCID: 0000-0001-6826-9901
  • Eliyahu Matzri
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia
  • Received by editor(s): June 5, 2013
  • Received by editor(s) in revised form: November 8, 2013, and January 29, 2014
  • Published electronically: March 11, 2015
  • Additional Notes: The first author was partially supported by NSF grants DMS-1007462 and DMS-1151252
    The second author was supported by the Israel Science Foundation (grant No. 152/13) and by the Kreitman Foundation
  • Communicated by: Lev Borisov
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 2779-2788
  • MSC (2010): Primary 12E30; Secondary 16K50, 17A05
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12461-6
  • MathSciNet review: 3336603