## Experimental Mathematics

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

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

Avner Ash, David Pollack, and Dayna Soares

#### 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

**Permanent link to this document**

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

**Keywords**

Galois representations arithmetic groups cohomology reciprocity laws Serre's conjecture

#### 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