Congruences between Ordinary Symplectic Galois Representations

Doctoral Dissertation

Abstract

We prove the existence of congruences between ordinary symplectic Galois representations in two different settings. First, we calculate lower bounds on the degree of the weight space map for Hida families given assumptions on the p-adic L-invariant (or the adjoint L-invariant) of a weight (3,3) automorphic representation on the Hida family when such an L-invariant is defined using theorems of Giovanni Rosso. Second, we set up a Galois deformation problem for a fixed absolutely irreducible Galois representation which is odd, ordinary and indecomposable at p, and unramified everywhere else. Under a mild local hypothesis, we prove the existence of at least two characteristic zero lifts of our fixed Galois representation.

Attributes

Attribute NameValues
Author Eric Wawerczyk
Contributor Andrei Jorza, Research Director
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name Doctor of Philosophy
Banner Code
  • PHD-MATH

Defense Date
  • 2019-04-01

Submission Date 2019-04-07
Record Visibility and Access Public
Content License
  • All rights reserved

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