Cohomology of moduli spaces via a result of Chenevier and Lannes

Abstract

We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with $\ell$-adic absolute Galois representations to determine the Euler characteristics (with values in the Grothendieck group of such representations) of ${\overline{\mathcal{M}}}_{3,n}$ and ${\mathcal{M}}_{3,n}$ for $n\le 14$ and of local systems ${\mathbb{V}}_{\lambda }$ on ${\mathcal{A}}_3$ for $|\lambda |\le 16$.

14 pages, minor revision

References in corpus (1)

• Remarks on the symmetric powers of cusp forms on GL(2)

Cited by in corpus (4)

• Extensions of tautological rings and motivic structures in the cohomology of ${\overline{\mathcal{M}}}_{g,n}$
• The eleventh cohomology group of ${\bar{\mathcal{M}}}_{g,n}$
• Weight 11 compactly supported cohomology of moduli spaces of curves
• Refinements of Katz-Sarnak theory for the number of points on curves over finite fields