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arXiv · 1508.05600

The stable cohomology of the Satake compactification of $\mathcal{A}_g$

Jiaming Chen·Eduard Looijenga
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Abstract

Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification the moduli space of principally polarized abelian varieties of dimension g stabilizes as g grows and they computed this stable cohomology as a Hopf algebra. We give a relatively simple algebro-geometric proof of their theorem that also takes into account the mixed Hodge structure that is present here. We find the latter to be impure.

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Jiaming Chen, Eduard Looijenga. 2016-09-10. The stable cohomology of the Satake compactification of $\mathcal{A}_g$. https://doi.org/10.2140/gt.2017.21.2231

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