Abstract:

 

Oort dened central leaves in the special ber of Shimura varieties as the locus on which the isomorphism class of the universal p-divisible group is constant (when Shimura varieties parametrize abelian varieties with additional structure). By employing geometric methods, Chia-Fu Yu proved irreducibility of leaves for Hilbert modular varieties, and Chai and Oort for Siegel modular varieties. In this talk I report on an ongoing project with Arno Kret on proving the irreducibility for Hodge-type Shimura varieties via a di erent approach using more automorphic input.