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

Kartik Prasanna; Akshay Venkatesh

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

Number Theory 2017-01-16 v2

Authors: Kartik Prasanna , Akshay Venkatesh

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.

Keywords

automorphic cohomology motivic cohomology adjoint L-function arithmetic groups Beilinson's conjecture

Cite

@article{arxiv.1609.06370,
  title  = {Automorphic cohomology, motivic cohomology, and the adjoint $L$-function},
  author = {Kartik Prasanna and Akshay Venkatesh},
  journal= {arXiv preprint arXiv:1609.06370},
  year   = {2017}
}

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

Abstract

Keywords

Cite

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