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Eichler-Shimura isomorphism and group cohomology on arithmetic groups (1701.00611v1)
Published 3 Jan 2017 in math.NT
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.