Admissible unitary completions of locally ℚ_{𝕡}-rational representations of 𝔾𝕃₂(𝔽)

Paškūnas, Vytautas

doi:10.1090/S1088-4165-10-00373-0

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

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

Published electronically: April 7, 2010

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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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