Points on Shimura varieties mod p

Monday, January 3, 2011 - 11:15am - 12:15pm
Keller 3-180
Mark Kisin (Harvard University)
I will explain some results towards the Langlands-Rapoport
conjecture which
predicts the structure of the mod p points of a Shimura
variety. A consequence
of the conjecture is that the isogeny class of every mod p
point contains a point which
admits a lifting to a special (ie CM) point of the Shimura
variety. One of the roots
of the subject is the work of John Tate on CM liftings and
endomorphisms of
abelian varieties mod p.