## 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