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Full-Text Articles in Physical Sciences and Mathematics
Comparison Of Three Dimensional Selfdual Representations By Faltings-Serre Method, Lian Duan
Comparison Of Three Dimensional Selfdual Representations By Faltings-Serre Method, Lian Duan
Doctoral Dissertations
In this thesis, we prove that, a selfdual 3-dimensional Galois representation constructed by van Geemen and Top is isomorphic to a quadratic twist of the symmetric square of the Tate module of an elliptic curve. This is an application of our refinement of the Faltings-Serre method to 3-dimensional Galois representations with ground field not equal to Q. The proof makes use of the Faltings-Serre method, $\ell$-adic Lie algebra, and Burnside groups.
Obstruction Criteria For Modular Deformation Problems, Jeffrey Hatley Jr
Obstruction Criteria For Modular Deformation Problems, Jeffrey Hatley Jr
Doctoral Dissertations
For a cuspidal newform f of weight k at least 3 and a prime p of the associated number field Kf, the deformation problem for its associated mod p Galois representation is unobstructed for all primes outside some finite set. Previous results gave an explicit bound on this finite set for f of squarefree level; we modify this bound and remove the squarefree hypothesis. We also show that if the p-adic deformation problem for f is unobstructed, then f is not congruent mod p to a newform of lower level.