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Proceedings of the American Mathematical Society

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

 
 

 

Diophantine and cohomological dimensions


Authors: Daniel Krashen and Eliyahu Matzri
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
Published electronically: March 11, 2015
MathSciNet review: 3336603
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Abstract | References | Similar Articles | Additional Information

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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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
Article copyright: © Copyright 2015 American Mathematical Society