Eichler Shimura isomorphism and group cohomology on arithmetic groups

JOURNAL OF NUMBER THEORY

卷:180

Article

Molina, Santiago¹ 

[1] CRM, Barcelona, Spain

关键词: Eichler-Shimura;    Automorphic forms;    Cohomology of arithmetic groups;    Automorphic representations;   

DOI  :  10.1016/j.jnt.2017.04.007

来源: Elsevier

【 摘 要 】

In this article, we give a group cohomological interpretation to the Eichler-Shimura isomorphism. For any quaternion algebra A over a totally real field with multiplicative group G, we interpret a weight (k(1), k(2), . . ., k(d))-automorphic form of G as a G(F)-invariant homomorphism of (g(infinity), K-infinity)-modules. Then the Eichler-Shimura isomorphism is given by the connection morphism provided by the natural exact sequences defining the (g(infinity), K-infinity)-module of discrete series of weight (k(1), k(2), ... , k(d)). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free