Compl\'et\'es universels de repr\'esentations de GL2(Qp)
Abstract
Let Pi be a unitary representation of GL2(Qp), topologically of finite length. We describe the sub-representation Pian 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 Pian is Pi itself.
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