24th Nordic and 1st Franco-Nordic Congress of Mathematicians

Cohomology of local systems on moduli spaces of curves and of abelian varieties

Carel Faber, Kungliga tekniska högskolan, Stockholm, Sweden

Abstract
The computation of the Σn-equivariant cohomology of the moduli space Mg,n of n-pointed curves of genus g can be reduced to that of the cohomology of local systems on Mg for the symplectic group Sp2g. These local systems are pulled back from local systems on the moduli space Ag of principally polarized abelian varieties of dimension g. Van der Geer and I have obtained explicit formulas for their cohomology, which are partly conjectural, in the case of genus 2. I will discuss these results as well as results in genus 3 obtained by Bergström. If time permits, I will also mention recent joint work with Consani.