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

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.

arXiv commentMinor revisions, submitted version

References in corpus (2)

• La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux
• A torsion Jacquet--Langlands correspondence

Cited by in corpus (3)

• Derived Hecke algebra and cohomology of arithmetic groups
• On the cohomology of GL(N) and adjoint Selmer groups
• Derived deformation rings allowing congruences]{Derived deformation rings allowing congruences