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Sur quelques représentations modulaires et p-adiques de GL2(Qp): I

(On Some Modular Representations and p-adics of

Published online by Cambridge University Press:  04 December 2007

Christophe Breuil
Christophe Breuil
Affiliation:
CNRS et IHES 35, route de Chartres, 91440 Bures-sur-Yvette, France. e-mail: breuil@ihes.fr
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Abstract

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Let p be a prime number and F a complete local field with residue field of characteristic p. In 1993, Barthel and Livné proved the existence of a new kind of $\overline{\bf F}_{p}$-representations of GL2(F) that they called ‘supersingular’ and on which one knows almost nothing. In this article, we determine all the supersingular representations of GL2(Qp) with their intertwinings. This classification shows a natural bijection between the set of isomorphism classes of supersingular representations of GL2(Qp) and the set of isomorphism classes of two-dimensional irreducible $\overline{\bf F}_{p}$-representations of ${\rm Gal}(\overline{\bf Q}_{p}/{\bf Q}_{p})$.

Keywords

supersingular representationsintertwinings
Type
Research Article
Information
Compositio Mathematica , Volume 138 , Issue 2 , September 2003 , pp. 165 - 188
Copyright
© 2003 Kluwer Academic Publishers