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arXiv · 1004.5462

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

Dan Petersen
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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.

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Dan Petersen. 2010-04-30. Cohomology of local systems on loci of d-elliptic abelian surfaces. https://doi.org/10.1307/mmj/1387226161

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