Duke Mathematical Journal

Galois representations with conjectural connections to arithmetic cohomology

Avner Ash, Darrin Doud, and David Pollack

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In this paper we extend a conjecture of A. Ash and W. Sinnott relating niveau 1 Galois representations to the $\mod p$ cohomology of congruence subgroups of ${\rm SL}\sb n(\mathbb {Z})$ to include Galois representations of higher niveau. We then present computational evidence for our conjecture in the case $n=3$ in the form of three-dimensional Galois representations which appear to correspond to cohomology eigenclasses as predicted by the conjecture. Our examples include Galois representations with nontrivial weight and level, as well as irreducible three-dimensional representations that are in no obvious way related to lower-dimensional representations. In addition, we prove that certain symmetric square representations are actually attached to cohomology eigenclasses predicted by the conjecture.

Article information

Duke Math. J., Volume 112, Number 3 (2002), 521-579.

First available in Project Euclid: 18 June 2004

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Zentralblatt MATH identifier

Primary: 11F75: Cohomology of arithmetic groups
Secondary: 11F60: Hecke-Petersson operators, differential operators (several variables) 11F80: Galois representations 11R39: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]


Ash, Avner; Doud, Darrin; Pollack, David. Galois representations with conjectural connections to arithmetic cohomology. Duke Math. J. 112 (2002), no. 3, 521--579. doi:10.1215/S0012-9074-02-11235-6. https://projecteuclid.org/euclid.dmj/1087575186

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