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2016•arXiv (Cornell University)Open access

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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What this paper is about

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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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Motivic cohomology, Mathematics, Cohomology, Pure mathematics, Group cohomology, Conjecture, Equivariant cohomology, De Rham cohomology

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