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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Capping groups and some cases of the Fontaine-Mazur conjecture
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by Frauke M. Bleher, Ted Chinburg and Jennifer Froelich PDF
Proc. Amer. Math. Soc. 137 (2009), 1551-1560

Abstract:

In this paper we will prove some cases of the Fontaine-Mazur conjecture. Let $p$ be an odd prime and let $G_{\mathbb {Q},\{p\}}$ be the Galois group over $\mathbb {Q}$ of the maximal unramified-outside-$p$ extension of $\mathbb {Q}$. We show that under certain hypotheses, the universal deformation of the action of $G_{\mathbb {Q},\{p\}}$ on the $2$-torsion of an elliptic curve defined over $\mathbb {Q}$ has finite image. We compute the associated universal deformation ring, and we show in the process that $\hat {S}_4$ caps $\mathbb {Q}$ for the prime $2$, where $\hat {S}_4$ is the double cover of $S_4$ whose Sylow $2$-subgroups are generalized quaternion groups.
References
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Additional Information
  • Frauke M. Bleher
  • Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
  • Email: fbleher@math.uiowa.edu
  • Ted Chinburg
  • Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
  • Email: ted@math.upenn.edu
  • Jennifer Froelich
  • Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
  • Address at time of publication: Department of Mathematics and Computer Science, Dickinson College, Carlisle, Pennsylvania 17013
  • Email: froelicj@dickinson.edu
  • Received by editor(s): April 14, 2008
  • Received by editor(s) in revised form: June 21, 2008
  • Published electronically: November 14, 2008
  • Additional Notes: The first author was supported in part by NSA Grant H98230-06-1-0021 and NSF Grant DMS06-51332.
    The second author was supported in part by NSF Grant DMS05-00106
  • Communicated by: Ken Ono
  • © Copyright 2008 Frauke M. Bleher, Ted Chinburg, and Jennifer Froelich
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1551-1560
  • MSC (2000): Primary 11R32; Secondary 20C05, 11G05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09677-9
  • MathSciNet review: 2470812