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

Date: 2021-09-16

Time: 15:30 - 16:30


Carel Faber


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.