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ISSN 1088-4165

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

Author(s): Vytautas Paskunas
Journal: Represent. Theory 14 (2010), 324-354.
MSC (2010): Primary 22-XX; Secondary 11-XX
Posted: April 7, 2010
MathSciNet review: 2608966
Retrieve article in: PDF

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Abstract: Let be a finite extension of $\mathbb{Q}_p$ , . We construct admissible unitary completions of certain representations of $\mathrm{GL}_2(F)$ on -vector spaces, where is a finite extension of . When $F=\mathbb{Q}_p$ using the results of Berger, Breuil and Colmez we obtain some results about lifting -dimensional mod representations of the absolute Galois group of $\mathbb{Q}_p$ to crystabelline representations with given Hodge-Tate weights.

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