skip to main content

Number Theory Seminar

Thursday, October 26, 2023
4:00pm to 5:00pm
Add to Cal
Linde Hall 387
On the Universal Deformation Ring of Residual Galois Representations with Three Jordan Holder Factors
Xiaoyu Huang, Graduate Center, City University of New York,

In this work, we study Fontaine-Laffaille, essentially self-dual deformations of a mod p non-semisimple Galois representation of dimension n with its Jordan-Holder factors being three mutually non-isomorphic absolutely irreducible representations. We show that under some conditions on certain Selmer groups, the universal deformation ring is a discrete valuation ring. Given enough information on the Hecke side, we also prove an R=T theorem. We then apply our results to abelian surfaces with cyclic rational isogenies and certain 6-dimensional representations arising from automorphic forms congruent to Ikeda lifts. In particular, our result identifies the special L-value conditions for the uniqueness of the abelian surface isogeny class, and assuming the Bloch-Kato conjecture, an R=T theorem for the 6-dimensional representations.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].