Cohomology of moduli spaces via a result of Chenevier and Lannes

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 $\ove...

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Bibliographic Details
Published inÉpijournal de géométrie algébrique Vol. 7
Main Authors Bergström, Jonas, Faber, Carel
Format Journal Article
LanguageEnglish
Published Association Epiga 03.10.2023
Subjects
14h10, 14k10
Automorphic representations
Euler characteristic
Galois representations
Hecke operators
Lefschetz trace formula
mathematics - algebraic geometry
moduli of abelian varieties
moduli of curves
Siegel modular forms
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Summary: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 $n \leq 14$ and of local systems $\mathbb{V}_{\lambda}$ on $\mathcal{A}_3$ for $|\lambda| \leq 16$.
ISSN:2491-6765
2491-6765
DOI:10.46298/epiga.2023.10307