Mathematical Research Letters

Volume 21 (2014)

Number 5

Cohomology of $GL_4 (\mathbb{Z})$ with nontrivial coefficients

Pages: 1111 – 1136



I. Horozov (Department of Mathematics, Washington University, Saint Louis, Missouri, U.S.A.)


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.

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