Automorphic cohomology, motivic cohomology, and the adjoint $L$-function

Kartik Prasanna; Akshay Venkatesh

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arXiv · 1609.06370

Automorphic cohomology, motivic cohomology, and the adjoint $L$-function

Kartik Prasanna·Akshay Venkatesh

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Abstract

We propose a relationship between the cohomology of arithmetic groups, and the motivic cohomology of certain (Langlands-)attached motives. The motivic cohomology group in question is that related, by Beilinson's conjecture, to the adjoint $L$-function at $s=1$. We present evidence for the conjecture using the theory of periods of automorphic forms, and using analytic torsion.

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Kartik Prasanna, Akshay Venkatesh. 2016-09-20. Automorphic cohomology, motivic cohomology, and the adjoint $L$-function. https://arxiv.org/abs/1609.06370

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