Admissible unitary completions of locally $Q_p$-rational representations of $GL_2(F)$

Details Admissible unitary completions of locally $Q_p$-rational representations of $GL_2(F)$ Admissible unitary completions of locally $Q_p$-rational representations of $GL_2(F)$

2008-05-07

arxiv.org/abs/0805.1006v1

Mathematics

Representation Theory

44 pages

Scientific paper

Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible unitary completions of certain representations of $GL_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results of Berger, Breuil and Colmez we obtain some results about lifting 2-dimensional mod $p$ representations of the absolute Galois group of $Q_p$ to crystabelline representations with given Hodge-Tate weights.

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