On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces, II.

On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces, II. We consider the cohomology of local systems on the moduli space of curves of genus 2 and the moduli space of Abelian surfaces. We dive an explicit formula for the Eisenstein cohomology and a conjectural formula for the endoscopic contribution. We show how, counting curves over finite fields provides Lis with detailed information about Siegel modular forms. (C) 2004 Academie des sciences. Publie par Elsevier SAS. Tous droits reserves.