Cuspidal cohomology of stacks of shtukas

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• Cong Xue (Cambridge)
• Tuesday 29 May 2018, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

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Let G be a split reductive group over a finite field Fq and X be a smooth projective geometrically irreducible curve over Fq.

We will recall the classifying stacks of G-shtukas and their l-adic cohomology, which is a generalisation of the space of automorphic forms with compact support for the function field of X. We will construct the constant term morphisms on the cohomology groups and define the cuspidal cohomology, which generalises the space of cuspidal automorphic forms. Then we will show that the cuspidal cohomology is of finite dimension and talk about some consequences related to the action of Hecke algebra.

This talk is part of the Number Theory Seminar series.

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