Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients

DOI10.1080/10586458.1998.10504381zbMath0923.11083OpenAlexW2050924553MaRDI QIDQ4236003

Avner Ash, Gerald Allison, Eric Conrad

Publication date: 22 April 1999

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/230980

zbMATH Keywords

Galois representationcharacteristic polynomialHecke eigenvaluesmod \(p\) cohomologydegree 3 homologyeigenclass

Mathematics Subject Classification ID

Galois representations (11F80) Cohomology of arithmetic groups (11F75)

Related Items (9)

Computing Heeke Eigenvalues Below the Cohomologieal Dimension ⋮ EVERYWHERE UNRAMIFIED AUTOMORPHIC COHOMOLOGY FOR SL₃(ℤ) ⋮ Homology of holomorphs of free groups. ⋮ Modular representations of \(\text{GL}(3,\mathbb{F}_p)\), symmetric squares, and mod-\(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\) ⋮ Symplectic modular symbols ⋮ An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the \(\operatorname{mod} p\) cohomology of \(\text{GL}(n,\mathbb{Z})\) ⋮ Galois representations with conjectural connections to arithmetic cohomology ⋮ Toward an explicit eigencurve for GL(3) ⋮ Cohomology of congruence subgroups of \(\text{SL}_4(\mathbb Z)\)

Cites Work

• Computations of cuspidal cohomology of congruence subgroups of SL(3,\({\mathbb{Z}})\)
• Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions
• Non-minimal modular symbols for GL(n)
• The modular symbol and continued fractions in higher dimensions
• Cohomology of congruence subgroups of \(SL(n,Z)\)
• Galois representations attached to mod \(p\) cohomology of \(GL(n,\mathbb{Z})\)
• The composition factors of \(F_ p[x_ 1, x_ 2, x_ 3\) as a \(GL(3, p)\)-module]
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra
• Heeke Eigenforms in the Cohomology of Congruence Subgroups of SL(3, Z)
• Galois representations and Hecke operators associated with the mod $p$ cohomology of $GL(1,\mathbb {Z})$ and $GL(2,\mathbb {Z})$
• Truncated symmetric powers and modular representations of GL_n
• Experimental Indications of Three-dimensional Galois Representations from the Cohomology of SL(3, Z)

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