Derived deformation rings allowing congruences]{Derived deformation rings allowing congruences
Yichang Cai
TL;DR
This paper extends the relationship between the cohomology of locally symmetric spaces and derived Galois deformation rings by removing previous restrictions and incorporating congruences within the Hecke algebra.
Contribution
It generalizes Galatius and Venkatesh's result by allowing congruences in the localized Hecke algebra and removing certain assumptions.
Findings
Established a broader connection between cohomology and derived deformation rings.
Allowed for congruences inside the localized Hecke algebra.
Removed previous assumptions in the theoretical framework.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models