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Transactions of the American Mathematical Society

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Formal constructions in the Brauer group of the function field of a $ p$-adic curve


Authors: Eric Brussel and Eduardo Tengan
Journal: Trans. Amer. Math. Soc. 367 (2015), 3299-3321
MSC (2010): Primary 11G20, 11R58, 14E22, 16K50
Published electronically: December 19, 2014
MathSciNet review: 3314809
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Abstract: We study the relationship between the cohomology of the function field of a curve over a complete discretely valued field and that of the function ring of curves resulting over its residue field. The results are applied to prove the existence of noncrossed product division algebras and indecomposable division algebras of unequal period and index over the function field of any $ p$-adic curve, generalizing the results and methods of a previous work of the authors and McKinnie.


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Additional Information

Eric Brussel
Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email: ebrussel@calpoly.edu

Eduardo Tengan
Affiliation: Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil
Email: etengan@icmc.usp.br

DOI: https://doi.org/10.1090/S0002-9947-2014-06154-0
Received by editor(s): March 21, 2012
Received by editor(s) in revised form: April 11, 2013
Published electronically: December 19, 2014
Additional Notes: The second author was supported by CNPq grant 303817/2011-9.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.