Doctoral Dissertations
Date of Award
2018
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
University
Columbia University
Department
Graduate School of Arts and Sciences
First Advisor
Eric Urban, Ph.D.
Keywords
Langlands program, automorphic forms, eigenvarieties, non-archimedean analysis
Subject Categories
Mathematics | Number Theory | Physical Sciences and Mathematics
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 Qp-analytic manifold taking values in a complete Tate Zp-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.
Recommended Citation
Gulotta, Daniel Robert '03, "Equidimensional Adic Eigenvarieties for Groups With Discrete Series" (2018). Doctoral Dissertations. 20.
https://digitalcommons.imsa.edu/alumni_dissertations/20