In mathematics we profit from the method of assigning an algebraic object (such as a number, a group, a ring, and so on) to a geometric object. Many proofs in geometry are unthinkable without this technique. Classification often starts by fixing an "invariant". Moving in a family we can study the behavior of "jumps" of the invariant.

In this talk the algebraic object will be a finite group scheme or a p-divisible group and the geometric objects considered are abelian varieties.

We give definitions, properties, examples, and open problems.

These methods give rise to geometric structures, when we keep these "invariants" fixed. We describe families of abelian varieties, of finite group schemes, of p-divisible groups.

### Algebra Seminar

Friday, March 2, 2018 - 3:15pm

#### Frans Oort

Utrecht University