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arXiv · 1301.7647

Complétés universels de représentations de GL_2(Q_p)

Pierre Colmez·Gabriel Dospinescu
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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.

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Pierre Colmez, Gabriel Dospinescu. 2013-01-31. Complétés universels de représentations de GL_2(Q_p). https://doi.org/10.2140/ant.2014.8.1447

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