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


Author: Vytautas Paskunas
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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Additional Information

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

DOI: http://dx.doi.org/10.1090/S1088-4165-10-00373-0
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.