Cohomology of the boundary of Siegel modular varieties of degree two, with applications

• Autorzy: J. William Hoffman , Steven H. Weintraub
• Języki publikacji: EN

Abstrakty

EN

Let 𝓐₂(n) = Γ₂(n)∖𝔖₂ be the quotient of Siegel's space of degree 2 by the principal congruence subgroup of level n in Sp(4,ℤ). This is the moduli space of principally polarized abelian surfaces with a level n structure. Let 𝓐₂(n)* denote the Igusa compactification of this space, and ∂𝓐₂(n)* = 𝓐₂(n)* - 𝓐₂(n) its "boundary". This is a divisor with normal crossings. The main result of this paper is the determination of H(∂𝓐₂(n)*) as a module over the finite group Γ₂(1)/Γ₂(n). As an application we compute the cohomology of the arithmetic group Γ₂(3).

Kategorie tematyczne

• 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
• 11F75: Cohomology of arithmetic groups
• 14G35: Modular and Shimura varieties
• 14J30: 3 -folds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 1
• Strony: 1-47

Daty

wydano

2003

Twórcy

autor

J. William Hoffman

• Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.

autor

Steven H. Weintraub

• Department of Mathematics, Lehigh University, Bethlehem, PA 18015, U.S.A.

Identyfikatory

DOI

10.4064/fm178-1-1