Experimental Mathematics

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

Avner Ash, David Pollack, and Dayna Soares

Full-text: Open access

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


Export citation