Vol. 13, No. 8, 2019

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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

We extend Urban’s construction of eigenvarieties for reductive groups G such that G() 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 p-analytic manifold taking values in a complete Tate 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.

eigenvarieties, spectral halo, nonarchimedean functional analysis
Mathematical Subject Classification 2010
Primary: 11F85
Secondary: 11S80
Received: 27 August 2018
Revised: 25 April 2019
Accepted: 24 June 2019
Published: 9 October 2019
Daniel R. Gulotta
Department of Mathematics
Columbia University
New York
Mathematical Institute
University of Oxford
United Kingdom