Cohomology of congruence subgroups of SL (4, Z) II

Avner Ash; Paul E. Gunnells; Mark McConnell

doi:10.1016/j.jnt.2007.09.002

Cohomology of congruence subgroups of SL (4, Z) II

Avner Ash, Paul E. Gunnells, Mark McConnell

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL₄ (Z), J. Number Theory 94 (2002) 181-212] we computed cohomology groups H⁵ (Γ₀ (N), C), where Γ₀ (N) is a certain congruence subgroup of SL (4, Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL₄ (Z), J. Number Theory 94 (2002) 181-212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL (4) concretely constructed in terms of Betti cohomology.

Original language	English (US)
Pages (from-to)	2263-2274
Number of pages	12
Journal	Journal of Number Theory
Volume	128
Issue number	8
DOIs	https://doi.org/10.1016/j.jnt.2007.09.002
State	Published - Aug 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Automorphic forms
Cohomology of arithmetic groups
Eisenstein cohomology
Hecke operators
Siegel modular forms

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10.1016/j.jnt.2007.09.002

Cite this

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title = "Cohomology of congruence subgroups of SL (4, Z) II",

abstract = "In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212] we computed cohomology groups H5 (Γ0 (N), C), where Γ0 (N) is a certain congruence subgroup of SL (4, Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL (4) concretely constructed in terms of Betti cohomology.",

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AU - Ash, Avner

AU - Gunnells, Paul E.

AU - McConnell, Mark

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AB - In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212] we computed cohomology groups H5 (Γ0 (N), C), where Γ0 (N) is a certain congruence subgroup of SL (4, Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4 (Z), J. Number Theory 94 (2002) 181-212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL (4) concretely constructed in terms of Betti cohomology.

KW - Automorphic forms

KW - Cohomology of arithmetic groups

KW - Eisenstein cohomology

KW - Hecke operators

KW - Siegel modular forms

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Cohomology of congruence subgroups of SL (4, Z) II

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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