Eichler-Shimura isomorphism and group cohomology on arithmetic groups

2017/01/03 by Blanco, Santiago Molina · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.00611

Abstract

The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we give a cohomological interpretation of the Eichler-Shimura isomorphism as a connection morphism of certain exact sequence of G-modules, for the multiplicative group G of any quaternion algebra over a totally real field.

Cited by

• Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh

Related

• Geometric and arithmetic theta correspondences
• Semisimplicity of étale cohomology of certain Shimura varieties
• Functorial splitting of l-adic cohomology in exact sequences of group varieties
• The Lambda-adic Eichler-Shimura isomorphism and p-adic etale cohomology
• Computing automorphic forms on Shimura curves over fields with arbitrary class number