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William Messing

2011-06-14
10:30:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

I. Finite locally-free commutative group schemes and Barsotti-Tate (= p-divisible) groups, initially over a general base scheme, S.

II. The classification of these groups when S = Spec(k), where k is a perfect field of characteristic zero (resp. p > 0). This, when p > 0, is the "classical" Dieudonne theory.

III. The case when S = Spec(R), R is a commuative ring in which all primes distinct from p are invertible and the groups are formal Lie groups of finite height. This is the Cartier theory via "typical curves".

IV. Crystalline Dieudonne theory where S is a scheme (resp. formal scheme) where p is locally nilpotent (resp. p is locally topologically nilpotent).

V. Applications to deformation theory of Basotti-Tate groups (resp. abelian schemes) and, in particular, the universal extensions and the Serre-Tate theorem.

VI. Zink's theory, further developed by Lau, of Displays and Dieudonne Displays.