CUNY Graduate Center
On the universal deformation ring of a residual Galois representation with three Jordan Holder factors and R = T theorems
In this work, we study Fontaine-Laffaille, essentially self-dual deformations of a mod p non-semisimple Galois representation with its Jordan-Holder factors being three mutually non-isomorphic absolutely irreducible representations. We establish sufficient conditions for the universal deformation ring to be a discrete valuation ring. We also get an R = T theorem given a bound on the appropriate Hecke congruence module. Potential applications to abelian surfaces with rational cycles and Ikeda lifts will be discussed.