Title: Cohomology of Abelian Varieties
Abstract: Abelian varieties
are compact complex tori that admit a holomorphic embedding into
projective space. As complex tori, their cohomology groups are
elementary to describe. On the other hand, describing the
cohomology classes that arise from algebraic sub-varieties is much more
difficult. In this talk I will focus on so-called minimal
cohomology classes in principally polarized abelian varieties.
The aim will be to introduce complex tori, discuss the example of
Jacobians, and outline some past work on the problem, including some
joint work with M. Popa and S. Schreieder.