Abstract
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 \({\bar F_p }\)-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(Q p ) with their intertwinings. This classification shows a natural bijection between the set of isomorphism classes of supersingular representations of GL2(Q p ) and the set of isomorphism classes of two-dimensional irreducible \({\bar F_p }\)-representations of \({Gal}\left( {{\bar Q}_p /{Q}_p } \right)\).
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Breuil, C. Sur quelques représentations modulaires et p-adiques de GL2(Q p ): I. Compositio Mathematica 138, 165–188 (2003). https://doi.org/10.1023/A:1026191928449
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DOI: https://doi.org/10.1023/A:1026191928449