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.