Cohomology of local systems on loci of d-elliptic abelian surfaces

Abstract

We consider the loci of d-elliptic curves in $M_2$, and corresponding loci of d-elliptic surfaces in $A_2$. We show how a description of these loci as quotients of a product of modular curves can be used to calculate cohomology of natural local systems on them, both as mixed Hodge structures and $\ell$-adic Galois representations. We study in particular the case d=2, and compute the Euler characteristic of the moduli space of n-pointed bi-elliptic genus 2 curves in the Grothendieck group of Hodge structures.

15 pages, complete re-write of earlier version

References in corpus (1)

• The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three

Cited by in corpus (2)

• The tautological ring of the space of pointed genus two curves of compact type
• Configuration spaces on a wedge of spheres and Hochschild-Pirashvili homology