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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-1,
author = {J. William Hoffman and Steven H. Weintraub},
title = {Cohomology of the boundary of Siegel modular varieties of degree two, with applications},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {1-47},
zbl = {1027.11038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-1}
}
J. William Hoffman; Steven H. Weintraub. Cohomology of the boundary of Siegel modular varieties of degree two, with applications. Fundamenta Mathematicae, Tome 177 (2003) pp. 1-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-1/