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Sur quelques repr\'esentations potentiellement cristallines de GL_2(Q_p)

L. Berger·C. Breuil
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Abstract

To each 2-dimensional irreducible p-adic representation of Gal(Qpbar/Qp) which becomes crystalline over an abelian extension of Q_p, we associate a Banach space B(V) endowed with a linear continuous unitary action of GL_2(Q_p). When V is moreover phi-semi-simple, we use the (phi,Gamma)-module and the Wach module associated to V to show that the representation B(V) is nonzero, topologically irreducible and admissible.

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L. Berger, C. Breuil. 2006-01-23. Sur quelques repr\'esentations potentiellement cristallines de GL_2(Q_p). https://arxiv.org/abs/math/0601545

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