On the cohomology of local systems on the moduli spaces of curves of genus 2 and of abelian surfaces. I

DOI10.1016/j.crma.2003.12.026zbMath1062.14034OpenAlexW2034466330MaRDI QIDQ1426625

Carel Faber, Gerard van der Geer

Publication date: 15 March 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.12.026

zbMATH Keywords

Siegel modular formsEisenstein cohomologyendoscopic contribution

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Algebraic moduli of abelian varieties, classification (14K10) Cohomology of arithmetic groups (11F75)

Related Items (19)

The rational cohomology of \(\overline{\mathcal{M}}_4\) ⋮ \(\mathrm{GL}_2\times \mathrm{GSp}_2\) \(L\)-values and Hecke eigenvalue congruences ⋮ Siegel modular forms of degree three and the cohomology of local systems ⋮ Traces des opérateurs de Hecke sur les espaces de formes automorphes de SO7, SO8 ou SO9 en niveau 1 et poids arbitraire ⋮ Cohomology of local systems on loci of \(d\)-elliptic abelian surfaces ⋮ The Gorenstein conjecture fails for the tautological ring of \(\overline{\mathcal{M}}_{2,n}\) ⋮ Some Siegel modular standard \(L\)-values, and Shafarevich-Tate groups ⋮ On zeta functions and families of Siegel modular forms ⋮ The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves ⋮ Siegel Modular Forms and Their Applications ⋮ Congruence Between a Siegel and an Elliptic Modular Form ⋮ Formal Fourier Jacobi expansions and special cycles of codimension two ⋮ Counting curves over finite fields ⋮ On vector-valued Siegel modular forms of degree 2 and weight \((j,2)\) ⋮ Eisenstein congruences for split reductive groups ⋮ Hecke eigenvalues of Siegel modular forms of ``different weights ⋮ Rank one Eisenstein cohomology of local systems on the moduli space of abelian varieties ⋮ SYMMETRIC SQUARE L-FUNCTIONS AND SHAFAREVICH–TATE GROUPS, II ⋮ On the homology of certain smooth covers of moduli spaces of algebraic curves

Cites Work

• An explicit dimension formula for the spaces of generalized automorphic forms with respect to \(\mathrm{Sp}(2, \mathbb Z)\)
• Vector valued Siegel's modular forms of degree two and the associated Andrianov \(L\)-functions
• On certain vector valued Siegel modular forms of degree two
• On \(\ell\)-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification
• Eisenstein cohomology and the construction of mixed motives
• On the \(l\)-adic cohomology of Siegel threefolds
• A regularized Siegel-Weil formula: The first term identity
• Motives for modular forms
• On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties
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