Hecke orbits on Shimura varieties of Hodge type

Pol van Hoften, Stanford University

Online Talk 

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits. 

Oort conjectured in 1995 that isogeny classes in the moduli space A_g of principally polarised abelian varieties in characteristic p are Zariski dense in the Newton strata containing them. There is a straightforward generalization of this conjecture to the special fibres of Shimura varieties of Hodge type, and in this talk, I will present a proof of this conjecture. I will mostly focus on the case of A_g since many of the new ideas can already be explained in this special case.

This is joint work with Marco D'Addezio.