Date of Award

2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

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.

Included in

Number Theory Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.