Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$
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Abstract:
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 $p$.References
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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: stefano.morra@univ-montp2.fr
- 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: https://doi.org/10.1090/S0002-9947-2013-05932-6
- MathSciNet review: 3105765