# Jun Su: Coherent cohomology of Shimura varieties and their automorphy

**Time: **
Wed 2022-06-01 13.15 - 14.15

**Location: **
Zoom, meeting ID: 694 6016 6420 (password required)

**Participating: **
Jun Su (Cambridge)

**Abstract:**

With modulars forms being the prototype, coherent cohomology groups of Shimura varieties make important bridges connecting Galois and automorphic representations. In non-proper cases these cohomology groups still have a nice formulation thanks to the local torus-bundle structures in Shimura varieties. Inspired by and analogous to Borel and Franke’s work on cohomology of local systems on locally symmetric spaces, we establish a Hecke equivariant isomorphism between these coherent cohomology and relative Lie algebra cohomology of automorphic forms.

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