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Algebra Seminar

Friday, May 3, 2019 - 3:15pm

Frans Oort

Utrecht University


University of Pennsylvania

4N36 DRL

Motivation. Isogenies with a polarized abelian variety give moduli points in a Hecke orbit. In characteristic zero any Hecke orbit is dense in this moduli space. What can be said about the Zariski closure of a Hecke orbit in positive characteristic?

This was the starting point for Ching-Li Chai who proved that for an ordinary abelian variety its Hecke orbit is dense (Inventiones Math. 1995) and for a conjecture that predicted the Zariski closure of any Hecke orbit (Questions in algebraic geometry, 1995).


Result. In joint work with Ching-Li Chai we prove this conjecture.  One of basic tools is the notion of  foliations. The main focus of the talk will be on describing properties of these foliations, rather well-understood by now.  Many other notions and previous results will be recalled in the proofs. We give examples and open questions.