2023/08/04 by Xiaoyu Huang, Huang, Xiaoyu
Mathematics · #11F55 #11F80 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2308.02708
openalex publication_date 2023/08/04 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28
In this paper, we study Fontaine-Laffaille, 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 regarding the orders of certain Selmer groups, the universal deformation ring is a discrete valuation ring. Given enough information on the Hecke algebra, we also prove an R = T theorem in the general context. 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. Assuming the Bloch-Kato conjecture, our result identifies special L-value conditions for the existence of a unique abelian surface isogeny class and an R = T theorem for certain 6-dimensional Galois representations.