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arXiv · 1510.03006

First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)

Lue Pan
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Abstract

We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve this, we generalize Breuil's work in the semi-stable case and work on the first covering of Drinfel'd upper half plane. Our main tool is an explicit semi-stable model of the first covering.

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Lue Pan. 2016-12-05. First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p). https://doi.org/10.2140/ant.2017.11.405

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