Cohomology of the boundary of Siegel modular varieties of degree two, with applications
Let A2(n) = Γ2(n)\G fraktur sign2 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 A 2(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).
Publication Source (Journal or Book title)
Hoffman, J., & Weintraub, S. (2003). Cohomology of the boundary of Siegel modular varieties of degree two, with applications. Fundamenta Mathematicae, 178 (1), 1-47. https://doi.org/10.4064/fm178-1-1