| In this talk we shall discuss the stable cohomology of A_g and its compactifications. It is a classical result of Borel that the cohomology of A_g stabilizes. This was extended to the Satake compactification by Charney and Lee. Looking at the rigid forms in the second Voronoi decomposition one sees that one cannot expect stable cohomology for the corresponding compactification. On the other hand we shall prove that the cohomology of the perfect cone compactification does stabilize. This is joint work with Orsola Tommasi and Sam Grushevsky. |