Contents Online
Mathematical Research Letters
Volume 21 (2014)
Number 5
Cohomology of $GL_4 (\mathbb{Z})$ with nontrivial coefficients
Pages: 1111 – 1136
DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n5.a9
Author
Abstract
We compute the cohomology groups of $GL_4 (\mathbb{Z})$ with coefficients in symmetric powers of the standard representation twisted by the determinant. This problem arises in Goncharov’s approach to the study of motivic multiple zeta values of depth $4$. We use a result of Harder on Eisenstein cohomology and a computationally effective version for the homological Euler characteristic of arithmetic groups.
Published 9 December 2014