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arXiv · 1310.2508

Cohomology of local systems on the moduli of principally polarized abelian surfaces

Dan Petersen
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Abstract

Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of Sp(4). We give an explicit expression for the cohomology of V in any degree in terms of Tate type classes and Galois representations attached to elliptic and Siegel cusp forms. This confirms a conjecture of Faber and van der Geer. As an application we prove a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, which had been conjectured by Ibukiyama.

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Dan Petersen. 2013-10-09. Cohomology of local systems on the moduli of principally polarized abelian surfaces. https://doi.org/10.2140/pjm.2015.275.39

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