Eigenvarieties and twisted eigenvarieties
Xiang
Zhengyu
author
Columbia University. Mathematics
Urban
Eric Jean-Paul
thesis advisor
Columbia University. Mathematics
Columbia University. Mathematics
originator
text
Dissertations
2012
English
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.
Ph.D., Columbia University.
Mathematics
http://hdl.handle.net/10022/AC:P:13124
NNC
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2012-05-03 14:44:03 -0400
2012-05-03 14:50:56 -0400
7127
eng