# Carel Faber: On the cohomology of moduli spaces of stable pointed curves: genus 4 and small n, and the vanishing of H^7 and H^9

Time: Thu 2021-09-16 15.30 - 16.30

Lecturer: Carel Faber (Universiteit Utrecht)

Abstract: Joint work with Jonas Bergström and Sam Payne.
For n at most 3, we determine the relevant terms of the point count of $$M_{4,n}$$ over finite fields ($$S_n$$-equivariantly). Using several earlier results, we then determine the cohomology of $$\overline{M}_{4,n}$$ and the full count for $$M_{4,n}$$ and we deduce the mentioned vanishing for all g and n.

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Last changed: Sep 15, 2021