Derived deformation rings and cohomology of locally symmetric spaces

Overview & Synopsis

We study derived Galois deformation functors and their derived deformation rings inrelation with the cohomology of locally symmetric spaces and derived Galois pseudodeformationfunctors. More precisely, in one text, we generalize a result of Galatius andVenkatesh, which relates the graded structure of cohomology of locally symmetric spacesto the graded homotopy ring of the derived Galois deformation rings, by removing certainassumptions, and in particular by allowing congruences inside the localized Hecke algebra.We also study in another text a derived analogue of Galois pseudo-deformation functorsin the sense of V. Laorgue in a purely algebraic approach, that is, independent of anautomorphic interpretation