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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: 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

Eliyahu Matzri
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia

DOI: https://doi.org/10.1090/S0002-9939-2015-12461-6
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