Euler characteristic and cohomology of ${\mathrm{Sp}}_4(\mathbb{Z})$ with nontrivial coefficients

Abstract

In this article, the cohomology of the arithmetic group ${\mathrm{Sp}}_4(\mathbb{Z})$ with coefficients in any finite dimensional highest weight representation ${\mathcal{M}}_{\lambda }$ have been studied. Euler characteristic with coefficients in ${\mathcal{M}}_{\lambda }$ have been carried out in detail. Combining the results obtained on Euler characteristic and the work of Harder on Eisenstein cohomology, the description of the cuspidal cohomology has been achieved. At the end, we employ our study to compute the dimensions for the cohomology spaces $H^{\bullet }({\mathrm{Sp}}_4(\mathbb{Z}),{\mathcal{M}}_{\lambda })$.

arXiv comment43 Pages. Article is revised. References are added

References in corpus (1)

• Cohomology of Siegel Varieties with p-adic integral coefficients and Applications