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arXiv · 1905.01547

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

Jitendra Bajpai·Ivan Horozov·Matias Moya Giusti
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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 $H^{\bullet}(\mathrm{Sp}_4(\mathbb{Z}), \mathcal{M}_\lambda)$.

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Jitendra Bajpai, Ivan Horozov, Matias Moya Giusti. 2019-05-04. Euler characteristic and cohomology of $\mathrm{Sp}_4(\mathbb{Z})$ with nontrivial coefficients. https://arxiv.org/abs/1905.01547

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