Derived deformation rings allowing congruences]Derived deformation rings allowing congruences

2021/08/30 by Yichang Cai, Cai, Yichang
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.13135

openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize a result of Galatius and Venkatesh which relates the graded module of cohomology of locally symmetric spaces to the graded homotopy ring of the derived Galois deformation rings, by removing certain assumptions, and in particular by allowing congruences inside the localized Hecke algebra.

Citations

• Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre
• Automorphic cohomology, motivic cohomology, and the adjoint L-function
• On the cohomology of GL(N) and adjoint Selmer groups

Related

• The Spectral Hecke Algebra
• Congruences between modular forms and related modules
• Serre weights, Galois deformation rings, and local models
• Generic smoothness for G-valued potentially semi-stable deformation rings
• Derived structures in the Langlands Correspondence