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

• DOI: 10.1307/mmj/1387226161
• Publication Date: 2013-12-16T20:36:15Z
• Authors: Dan Petersen
• Keywords: Mathematics - Number Theory; 15K10; 14G35; 11F11; 11F41; 01 natural sciences; Mathematics - Algebraic Geometry; FOS: Mathematics; 14J15, 14G35, 11F11; Number Theory (math.NT); 0101 mathematics; Algebraic Geometry (math.AG)

15 pages, complete re-write of earlier version<br/>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.<br/>