HomeHome

Eigenvarieties and twisted eigenvarieties

Zhengyu Xiang

Title:
Eigenvarieties and twisted eigenvarieties
Author(s):
Xiang, Zhengyu
Thesis Advisor(s):
Urban, Eric Jean-Paul
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
For an arbitrary reductive group G, we construct the full eigenvariety E, which parameterizes all p-adic overconvergent cohomological eigenforms of G in the sense of Ash-Stevens and Urban. Further, given an algebraic automorphism a of G, we construct the twisted eigenvariety E^a, a rigid subspace of E, which parameterizes all eigenforms that are invariant under a. In particular, in the case G = GLn, we prove that every self-dual automorphic representation can be deformed into a family of self-dual cuspidal forms containing a Zariski dense subset of classical points. This is the inverse of Ash-Pollack-Stevens conjecture. We also give some hint to this conjecture.
Subject(s):
Mathematics
Item views
726
Metadata:
text | xml
Suggested Citation:
Zhengyu Xiang, , Eigenvarieties and twisted eigenvarieties, Columbia University Academic Commons, .

Columbia University Libraries | Policies | FAQ