Cohomology of the boundary of Siegel modular varieties of degree two, with applications
Fundamenta Mathematicae, Tome 178 (2003) no. 1, p. 1.

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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).
Classification : 14G35, 11F46, 11F75, 14J30
Mots-clés : Siegel modular varieties, moduli spaces, group cohomology 
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J. William Hoffman; Steven H. Weintraub. Cohomology of the boundary of Siegel modular varieties of degree two, with applications. Fundamenta Mathematicae, Tome 178 (2003) no. 1, p. 1. https://geodesic-test.mathdoc.fr/item/FUNDAM_2003__178_1_283274/