Geometry and Arithmetic
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In his paper , Gerard van der Geer discusses the Eisenstein cohomology with coefficients in a sheaf $\tilde M$, which is obtained from a representation for the group $\tilde\Gamma=\GSp_g(\mathbb Z)$. 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 $g=2$ and a regular coefficient system , 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 $g=2$.
Keywords: Shimura varieties, L-functions, motives