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

Jitendra Bajpai; Ivan Horozov; Matias Moya Giusti

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

Number Theory 2021-07-15 v2

Authors: Jitendra Bajpai , Ivan Horozov , Matias Moya Giusti

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 $H^{\bullet}(\mathrm{Sp}_4(\mathbb{Z}), \mathcal{M}_\lambda)$ .

Keywords

arithmetic groups sp4(z) euler characteristic cohomology highest weight representation cuspidal cohomology eisenstein cohomology

Cite

@article{arxiv.1905.01547,
  title  = {Euler characteristic and cohomology of $\mathrm{Sp}_4(\mathbb{Z})$ with nontrivial coefficients},
  author = {Jitendra Bajpai and Ivan Horozov and Matias Moya Giusti},
  journal= {arXiv preprint arXiv:1905.01547},
  year   = {2021}
}

Comments

43 Pages. Article is revised. References are added

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

Abstract

Keywords

Cite

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