On The Stable Cohomology Of The Satake Compactification And Its Mixed Hodge Structure

In this paper we are concerned with the stable cohomology of the Satake compactification of the coarse moduli space of principally polarized abelian varieties and its mixed Hodge structure. In particular, we provide a more transparent proof of the Charney-Lee stability theorem using the categorical description of the rational homotopy type of Abb gand determine the Hodge type of the ?-classes.