Department of Mathematics


  •  Tony Feng, MIT
  •  The Spectral Hecke Algebra
  •  01/29/2020
  •  3:00 PM - 4:00 PM
  •  C304 Wells Hall

We introduce a derived enhancement of local Galois deformation rings that we call the “spectral Hecke algebra”, in analogy to a construction in the Geometric Langlands program. This is a Hecke algebra that acts on the spectral side of the Langlands correspondence, i.e. on moduli spaces of Galois representations. We verify the simplest form of derived local-global compatibility between the action of the spectral Hecke algebra on the derived Galois deformation ring of Galatius-Venkatesh, and the action of Venkatesh’s derived Hecke algebra on the cohomology of arithmetic groups.



Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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College of Natural Science