#### 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
##### Abstract

We extend Urban’s construction of eigenvarieties for reductive groups $G$ such that $G\left(ℝ\right)$ 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.

##### Keywords
eigenvarieties, spectral halo, nonarchimedean functional analysis
Primary: 11F85
Secondary: 11S80