Résumé: This is joint work with Carel Faber (KTH, Stockholm). In the talk
we will deal with the cohomology of local systems on the moduli space of
curves of genus 2 and the moduli space of abelian surfaces.
We describe explicitly the contributions from the boundary and
endoscopy and we shall show how counting curves over finite fields
provides us with detailed information about Siegel modular forms.