Workshop on Eisenstein Series, L-functions, and arithmetic, May 2022



Xiaoyu Huang


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. 


Benedum G-29

May 17, 2022 - 11:30am to 12:00pm