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

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.