Equidimensional adic eigenvarities for groups with discrete series

Journal article

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 $p$ -analytic manifold taking values in a complete Tate ${\mathbb{Z}}_p$ -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.

Authors: Gulotta, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Mathematical Sciences Publishers
• Journal: Algebra and Number Theory
• Volume: 13
• Issue: 8
• Pages: 1907–1940
• Publication date: 2019-10-09
• Acceptance date: 2019-06-24
• DOI: 10.2140/ant.2019.13.1907
• EISSN: 1944-7833
• ISSN: 1937-0652
• Keywords: SBTMR; spectral halo; nonarchimedean functional analysis; eigenvarieties