Derived Galois deformation rings
By Søren Galatius, Akshay Venkatesh. 2016
54 citations recorded by the source corpus.
Abstract We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring R classifying deformations of a fixed Galois representation to simplicial coefficient rings; its zeroth homotopy group π 0 R recovers Mazur's deformation ring. We give evidence that these rings R occur in the wild: For suitable Galois representations, the Langlands program predicts that π 0 R should act on the homology of an arithmetic group. We explain how the Taylor–Wiles method can be used to upgrade such an action to a graded action of π ⁎ R on the homology.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/530aa33f16ac3e7af71ed699b0c67efb433435ed
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Coherent sheaves on the stack of Langlands parameters (2020, background): “ C cts( ;Ad ˆ) := lim! i C( i;Ad ˆ) denotes the continuous cohomology and C cts( ;Ad ˆ)[1] is its reduced version. Next we relate Rc ;M with the usual deformation space (and its derived version as in [GV18]). In the rest of this subsection, we assume that Mis an ane smooth group scheme over O E. We ”