Sur la cohomologie des systèmes locaux sur les espaces des modules des courbes de genre 2 et des surfaces abéliennes

Abstract

We consider the cohomology of local systems on the moduli space of curves of genus 2 and the moduli space of abelian surfaces. We give an explicit formula for the Eisenstein cohomology and a conjectural formula for the endoscopic contribution. We show how counting curves over finite fields provides us with detailed information about Siegel modular forms.

arXiv comment7 pages

Cited by in corpus (10)

• Tautological and non-tautological cohomology of the moduli space of curves
• The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
• Generators for modules of vector-valued Picard modular forms
• The cohomology of the moduli space of abelian varieties
• Siegel modular forms of genus 2 and level 2
• The equivariant Euler characteristic of moduli spaces of curves
• Exploring modular forms and the cohomology of local systems on moduli spaces by counting points
• Rank one Eisenstein cohomology of local systems on the moduli space of abelian varieties
• The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves
• Counting curves over finite fields