Equidimensional adic eigenvarieties for groups with discrete series

Gulotta, Daniel R.

doi:10.2140/ant.2019.13.1907

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Equidimensional adic eigenvarieties for groups with discrete series

Daniel R. Gulotta

Vol. 13 (2019), No. 8, 1907–1940

DOI: 10.2140/ant.2019.13.1907

Abstract

We extend Urban’s construction of eigenvarieties for reductive groups $G$ such that $G (ℝ)$ has discrete series to include characteristic $p$ points at the boundary of weight space. In order to perform this construction, we define a notion of “locally analytic” functions and distributions on a locally $ℚ_{p}$ -analytic manifold taking values in a complete Tate $ℤ_{p}$ -algebra in which $p$ is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on $p$ -adic Lie groups given by Johansson and Newton.

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Keywords

eigenvarieties, spectral halo, nonarchimedean functional analysis

Mathematical Subject Classification 2010

Primary: 11F85

Secondary: 11S80

Milestones

Received: 27 August 2018

Revised: 25 April 2019

Accepted: 24 June 2019

Published: 9 October 2019

Authors

Daniel R. Gulotta
Department of Mathematics Columbia University New York USA	Mathematical Institute University of Oxford United Kingdom

Vol. 13, No. 8, 2019