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

J. William Hoffman, and Steven H. Weintraub. "Cohomology of the boundary of Siegel modular varieties of degree two, with applications." Fundamenta Mathematicae 178.1 (2003): 1-47. <http://eudml.org/doc/283274>.

@article{J2003,
abstract = {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).},
author = {J. William Hoffman, Steven H. Weintraub},
journal = {Fundamenta Mathematicae},
keywords = {Siegel modular varieties; moduli spaces; group cohomology},
language = {eng},
number = {1},
pages = {1-47},
title = {Cohomology of the boundary of Siegel modular varieties of degree two, with applications},
url = {http://eudml.org/doc/283274},
volume = {178},
year = {2003},
}

TY - JOUR
AU - J. William Hoffman
AU - Steven H. Weintraub
TI - Cohomology of the boundary of Siegel modular varieties of degree two, with applications
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 1
SP - 1
EP - 47
AB - 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).
LA - eng
KW - Siegel modular varieties; moduli spaces; group cohomology
UR - http://eudml.org/doc/283274
ER -