## Duke Mathematical Journal

### Galois representations with conjectural connections to arithmetic cohomology

#### Abstract

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

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

Dates
First available in Project Euclid: 18 June 2004

http://projecteuclid.org/euclid.dmj/1087575186

Digital Object Identifier
doi:10.1215/S0012-9074-02-11235-6

Mathematical Reviews number (MathSciNet)
MR1896473

Zentralblatt MATH identifier
1023.11025

#### Citation

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. http://projecteuclid.org/euclid.dmj/1087575186.

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