Sur quelques représentations potentiellement cristallines de GL_2(Q_p)

Details Sur quelques représentations potentiellement cristallines de GL_2(Q_p) Sur quelques représentations potentiellement cristallines de GL_2(Q_p)

2006-01-23

arxiv.org/abs/math/0601545v1

Asterisque 330 (2010), 155--211.

Mathematics

Number Theory

Scientific paper

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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