The topology of $A_g$ and its compactifications

15 May 2018  ·  Hulek Klaus, Tommasi Orsola ·

We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and on stabilization results... We review both geometric and representation theoretic approaches to the problem. The appendix provides a detailed discussion of computational methods based on trace formulae and automorphic representations, in particular Arthur's endoscopic classification of automorphic representations for symplectic groups. read more

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Algebraic Geometry