Eigenvarieties and twisted eigenvarieties
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.
AC:P:13124
Academic Commons
Xiang, Zhengyu
Author
Urban, Eric Jean-Paul
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2012
eng
2017-06-07T17:02:23Z
2017-11-10T04:43:51Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8H41ZKN