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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$
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by Stefano Morra PDF
Trans. Amer. Math. Soc. 365 (2013), 6625-6667 Request permission


Let $p$ be an odd rational prime and $F$ a $p$-adic field. We give a realization of the universal $p$-modular representations of ${\mathbf {GL}}_{2}(F)$ in terms of an explicit Iwasawa module. We specialize our constructions to the case $F={\mathbf {Q}}_p$, giving a detailed description of the invariants under principal congruence subgroups of irreducible admissible $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$, generalizing previous work of Breuil and Paskunas. We apply these results to the local-global compatibility of Emerton, giving a generalization of the classical multiplicity one results for the Jacobians of modular curves with arbitrary level at $p$.
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Additional Information
  • Stefano Morra
  • Affiliation: Laboratoire de Mathématiques de Montpellier, place Eugène Bataillon, Case courrier 051, 34095 Montpellier cedex 5, France
  • Address at time of publication: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
  • Email:
  • Received by editor(s): February 14, 2010
  • Received by editor(s) in revised form: April 11, 2012, May 6, 2012, July 2, 2012, and August 6, 2012
  • Published electronically: July 10, 2013
  • Additional Notes: The author was partially supported by a Fields-Ontario Postdoctoral Fellowship
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6625-6667
  • MSC (2010): Primary 22E50, 11F85
  • DOI:
  • MathSciNet review: 3105765