Euler characteristic and cohomology of \Sp₄(\ℤ) with\n nontrivial coefficients

2019/05/04 by Jitendra Bajpai, Bajpai, Jitendra, Ivan Horozov +3
Mathematics · #11F06 #11F22 #11F70 #11F75 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.01547

openalex publication_date 2019/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, the cohomology of the arithmetic group\n\Sp₄(\ℤ) with coefficients in any finite dimensional highest\nweight representation \M_\λ have been studied. Euler\ncharacteristic with coefficients in \M_\λ have been carried out\nin detail. Combining the results obtained on Euler characteristic and the work\nof Harder on Eisenstein cohomology, the description of the cuspidal cohomology\nhas been achieved. At the end, we employ our study to compute the dimensions\nfor the cohomology spaces H ^bullet(\Sp₄(\ℤ),\n\M_\λ).\n

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