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Algebra Seminar

Friday, November 19, 2021 - 3:30pm

Tao Song

University of Pennsylvania


University of Pennsylvania


When we look at the moduli space of abelian varieties, some 'linear spaces' naturally pop up. A classical example is the Serre-Tate coordinates, which says that the local deformation space of an ordinary abelian variety is a formal torus. 'Linear subspaces' of the Serre-Tates coordinates, i.e. sub-tori, are interesting due to the connection with Shimura subvarieties.  Ching-Li Chai and Frans Oort defined the notion of sustained p-divisible groups and sustained deformation spaces of abelian varieties, which provides a scheme-theoretic definition of central leaves in moduli spaces. These sustained deformation spaces are 'linear spaces' that generalize the Serre-Tate coordinates, and the strong rigidity conjecture is a conjecture that relates to their 'linear subspaces'.  
We give definitions, properties, examples, and report some progress on the strong rigidity conjecture.