WawerczykEN042019D.pdf (435.49 kB)
Congruences between Ordinary Symplectic Galois Representations
thesis
posted on 2019-04-07, 00:00 authored by Eric WawerczykWe 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.
History
Date Modified
2019-06-27Defense Date
2019-04-01CIP Code
- 27.0101
Research Director(s)
Andrei JorzaDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Alternate Identifier
1105810958Library Record
5113945OCLC Number
1105810958Program Name
- Mathematics
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