The Eisenstein motive for the cohomology of GSp<sub>2</sub>(ℤ)

  • Günter Harder

    Universität Bonn, Germany
The Eisenstein motive for the cohomology of GSp<sub>2</sub>(ℤ) cover
Download Chapter PDF

A subscription is required to access this book chapter.

Abstract

In his paper [4], Gerard van der Geer discusses the Eisenstein cohomology with coefficients in a sheaf M~\tilde M, which is obtained from a representation for the group Γ~=\GSpg(Z)\tilde\Gamma=\GSp_g(\mathbb Z). Since we have an arithmetic interpretation of this sheaf, we can endow these cohomology groups with the structure of a mixed motive. A certain part of this cohomology is the compactly supported Eisenstein cohomology and van der Geer determines the structure of this compactly supported Eisenstein motive in the case g=2g=2 and a regular coefficient system [4], Cor.~10.2). At the end of this note we compute this part of the cohomology for an arbitrary coefficient system, again in the case g=2g=2.