Resolutions of the Steinberg module for \(\mathrm{GL}(n)\)

DOI10.1016/j.jalgebra.2011.09.018zbMath1294.11077arXiv1106.5034OpenAlexW1492585396MaRDI QIDQ420704

Avner Ash, Paul E. Gunnells, Mark McConnell

Publication date: 23 May 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5034

zbMATH Keywords

modular symbolscohomology of arithmetic groupsSteinberg moduleVoronoi complex

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Cohomology theory for linear algebraic groups (20G10) Cohomology of arithmetic groups (11F75)

Related Items

Galois representations attached to tensor products of arithmetic cohomology ⋮ Mod p Base Change transfer for GL(2) ⋮ Comparison of Steinberg modules for a field and a subfield ⋮ Steinberg homology, modular forms, and real quadratic fields ⋮ The Steinberg representation is irreducible ⋮ Cohomology of congruence subgroups of \(\mathrm{SL}_3(\mathbb{Z})\), Steinberg modules, and real quadratic fields ⋮ Mod 2 homology for \(\mathrm{GL}(4)\) and Galois representations ⋮ MODULAR FORMS AND ELLIPTIC CURVES OVER THE CUBIC FIELD OF DISCRIMINANT –23 ⋮ Modular elliptic curves over the field of twelfth roots of unity ⋮ ON THE GROWTH OF TORSION IN THE COHOMOLOGY OF ARITHMETIC GROUPS ⋮ Cohomology with twisted one-dimensional coefficients for congruence subgroups of \(\operatorname{SL}_4(\mathbb{Z})\) and Galois representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Torsion in the cohomology of congruence subgroups of \(\text{SL}(4, \mathbb Z)\) and Galois representations
• Classical projective geometry and arithmetic groups
• Cohomology of congruence subgroups of \(\text{SL}(4,\mathbb Z)\). II
• The modular symbol and continued fractions in higher dimensions
• Unstable cohomology of \(SL(n,O)\)
• Cohomology of congruence subgroups of \(\text{SL}_4(\mathbb Z)\)
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Cohomology of congruence subgroups of $ {SL}_4(\mathbb {Z})$. III
• Computing Heeke Eigenvalues Below the Cohomologieal Dimension
• On the homology and cohomology of congruence subgroups