Equidimensional adic eigenvarieties for groups with discrete series

DOI10.2140/ANT.2019.13.1907arXiv1707.05302WikidataQ127075201 ScholiaQ127075201MaRDI QIDQ6289111

Daniel R. Gulotta

Publication date: 17 July 2017

Abstract: We extend Urban's construction of eigenvarieties for reductive groups $G$ such that $G(mathbbR)$ 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 $mathbb{Q}_p$-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.

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) (p)-adic theory, local fields (11F85) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

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