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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Admissible unitary completions of locally $\mathbb {Q}_p$-rational representations of $\mathrm {GL}_2(F)$
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by Vytautas Paškūnas
Represent. Theory 14 (2010), 324-354
Published electronically: April 7, 2010


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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Bibliographic Information
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 324-354
  • MSC (2010): Primary 22-XX; Secondary 11-XX
  • DOI:
  • MathSciNet review: 2608966