## Experimental Mathematics

### $\SL_3(\F_2)$-Extensions of $\Q$ and Arithmetic Cohomology Modulo 2

#### Abstract

We generate extensions of $\Q$ with Galois group $\SL_3(\F_2)$ giving rise to three-dimensional mod 2 Galois representations with sufficiently low level to allow the computational testing of a conjecture of Ash, Doud, Pollack, and Sinnott relating such representations to mod 2 arithmetic cohomology. We test the conjecture for these examples and offer a refinement of the conjecture that resolves ambiguities in the predicted weight.

#### Article information

Source
Experiment. Math., Volume 13, Issue 3 (2004), 297-307.

Dates
First available in Project Euclid: 22 December 2004

https://projecteuclid.org/euclid.em/1103749838

Mathematical Reviews number (MathSciNet)
MR2103328

Zentralblatt MATH identifier
1094.11019

Subjects
Primary: 11F80: Galois representations
Secondary: 11F75: Cohomology of arithmetic groups

#### Citation

Ash, Avner; Pollack, David; Soares, Dayna. $\SL_3(\F_2)$-Extensions of $\Q$ and Arithmetic Cohomology Modulo 2. Experiment. Math. 13 (2004), no. 3, 297--307. https://projecteuclid.org/euclid.em/1103749838