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Finite group schemes and p-divisible groups
Finite Group Schemes and p-Divisible Groups
Last Updated: 2026-02-05 14:55:07
Abstract
Classification of finite commutative group schemes and p-divisible groups over a perfect field of characteristic p. We present the classical approach by contravariant Dieudonné theory.Group schemes, p-divisible groups, Cartier duality, Frobenius, Verschiebung, Witt vectors, Artin-Hasse exponential, rational Dieudonne modules, slopes, inner Hom, multilinear Dieudonné theory
Objective
The main topic of the course is the classification of finite commutative group schemes and p-divisible groups over a perfect field of characteristic p. We present the classical approach by contravariant Dieudonné theory. Other methods such as Cartier theory, and newer results about the classification over schemes in terms of crystals and/or displays might be topics for a continuation in the Sommersemester 2005. Finite group schemes and p-divisible groups are important for the study of abelian varieties.
Content
Provisional content: 1. Group schemes, categorical properties, quotients, descent 2. Finite flat group schemes, Cartier duality, Frobenius, Verschiebung 3. Ind group schemes, p-divisible groups 4. Witt vectors, Artin-Hasse exponential 5. Contravariant Dieudonné theory, equivalence of categories 6. p-divisible groups up to isogeny, rational Dieudonne modules, slopes 7. Inner Hom, multilinear Dieudonné theory
Resources
Lecture Notes
no script
Literature
Demazure, Michel: Lectures on p-Divisible Groups. Lecture Notes in Mathematics 302, Berlin et al.: Springer 1972 Additional literature will be indicated during the course.
General Information
- Language
- English
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Finite Group Schemes and p-Divisible Groups |
|
2 h weekly |