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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Formal constructions in the Brauer group of the function field of a $p$-adic curve
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by Eric Brussel and Eduardo Tengan PDF
Trans. Amer. Math. Soc. 367 (2015), 3299-3321 Request permission

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
  • 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.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 3299-3321
  • MSC (2010): Primary 11G20, 11R58, 14E22, 16K50
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06154-0
  • MathSciNet review: 3314809