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

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Hoffman J., Weintraub S.

Fundamenta Mathematicae

2003

tom 178

nr 1

1-47

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).

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Hoffman J.

1 Weintraub S.

1 2003

Wyniki wyszukiwania

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