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Eigenvarieties and twisted eigenvarieties

Zhengyu Xiang

Title:
Eigenvarieties and twisted eigenvarieties
Author(s):
Xiang, Zhengyu
Thesis Advisor(s):
Urban, Eric Jean-Paul
Date:
Type:
Dissertations
Department:
Mathematics
Permanent URL:
Notes:
Ph.D., Columbia University.
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:
226
Metadata:
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