Compl\'et\'es universels de repr\'esentations de GL_2(Q_p)
Number Theory
2016-01-20 v1 Representation Theory
Abstract
Let Pi be a unitary representation of GL_2(Q_p), topologically of finite length. We describe the sub-representation Pi^{an} made of its locally analytic vectors, and its filtration by radius of analyticity, in terms of the phi-Gamma module attached to Pi via the p-adic local Langlands correspondence, and we deduce that the universal completion of Pi^{an} is Pi itself.
Keywords
Cite
@article{arxiv.1301.7647,
title = {Compl\'et\'es universels de repr\'esentations de GL_2(Q_p)},
author = {Pierre Colmez and Gabriel Dospinescu},
journal= {arXiv preprint arXiv:1301.7647},
year = {2016}
}
Comments
65 pages, in French, submitted