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Admissible unitary completions of locally $\mathbb {Q}_p$-rational representations of $\mathrm {GL}_2(F)$

Author: Vytautas Paškūnas
Journal: Represent. Theory 14 (2010), 324-354
MSC (2010): Primary 22-XX; Secondary 11-XX
Published electronically: April 7, 2010
MathSciNet review: 2608966
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Abstract: Let $F$ be a finite extension of $\mathbb {Q}_p$, $p>2$. We construct admissible unitary completions of certain representations of $\mathrm {GL}_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=\mathbb {Q}_p$ 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 $\mathbb {Q}_p$ to crystabelline representations with given Hodge-Tate weights.

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Vytautas Paškūnas
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

Received by editor(s): September 15, 2008
Published electronically: April 7, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.