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# Sam Grushevsky : Stable cohomology of compactifications of the moduli spaces of abelian varieties

Cohomology of A_g, the moduli space of principally polarized complex g-dimensional abelian varieties, is the same as the cohomology of Sp(2g,Z). By Borel's result on group homology it turns out that for g>k the cohomology H^k(A_g) is independent of g - it is then called the stable cohomology of A_g. Similarly, the stable cohomology of the moduli space of curves was the subject of Mumford's conjecture, proven by Madsen and Weiss by topological methods. In a joint work with Klaus Hulek and Orsola Tommasi we show that the cohomology of the perfect cone toroidal compactification of A_g stabilizes, and compute some of this stable cohomology using algebro-geometric methods.

**Category**: Algebraic Geometry**Duration**: 01:34:55**Date**: March 6, 2013 at 4:25 PM**Views**: 134-
**Tags:**seminar, Algebraic Geometry Seminar

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