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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Conductors of wild extensions of local fields, especially in mixed characteristic $(0,2)$
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by Andrew Obus PDF
Proc. Amer. Math. Soc. 142 (2014), 1485-1495 Request permission

Abstract:

If $K_0$ is the fraction field of the Witt vectors over an algebraically closed field $k$ of characteristic $p$, we calculate upper bounds on the conductor of higher ramification for (the Galois closure of) extensions of the form $K_0(\zeta _{p^c}, \sqrt [p^c]{a})/K_0$, where $a \in K_0(\zeta _{p^c})$. Here $\zeta _{p^c}$ is a primitive $p^c$th root of unity. In certain cases, including when $a \in K_0$ and $p=2$, we calculate the conductor exactly. These calculations can be used to determine the discriminants of various extensions of $\mathbb {Q}$ obtained by adjoining roots of unity and radicals.
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Additional Information
  • Andrew Obus
  • Affiliation: Department of Mathematics, MC4403, Columbia University, 2990 Broadway, New York, New York 10027
  • Address at time of publication: Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, Virginia 229904-4137
  • MR Author ID: 890287
  • ORCID: 0000-0003-2358-4726
  • Email: obus@virginia.edu
  • Received by editor(s): October 2, 2011
  • Received by editor(s) in revised form: May 29, 2012
  • Published electronically: February 4, 2014
  • Additional Notes: The author was supported by an NSF Postdoctoral Research Fellowship in the Mathematical Sciences. Final preparation of this paper took place at the Max-Planck-Institut für Mathematik in Bonn
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 1485-1495
  • MSC (2010): Primary 11S15, 11S20; Secondary 11R18, 11R20, 12F05, 12F10
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11881-8
  • MathSciNet review: 3168456