Title

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

Document Type

Article

Publication Date

1-1-2003

Abstract

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)

Fundamenta Mathematicae

First Page

1

Last Page

47

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