Doctoral Dissertations

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Columbia University


Graduate School of Arts and Sciences

First Advisor

Eric Urban, Ph.D.


Langlands program, automorphic forms, eigenvarieties, non-archimedean analysis

Subject Categories

Mathematics | Number Theory | Physical Sciences and Mathematics


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



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