Dieudonné theory: from classical to prismatic
Finite flat group schemes and $p$-divisible groups are fundamental objects in arithmetic geometry, as they arise in studying ($p$-power) torsion points of abelian varieties. Dieudonné theory provides an explicit way to understand finite flat group schemes / $p$-divisible groups via concrete linear algebraic objects, and thereby has wide-ranging applications in arithmetic geometry. This course will give an overview of Dieudonné theory, from classical results to modern developments. We will begin with foundations on finite flat group schemes / $p$-divisible groups, and study the classical results due to Dieudonné, Fontaine, Berthelot, and others. Then we will move on to discussing the result of Scholze-Weinstein, and give a quick overview of the prismatic Dieudonné theory due to Anschütz-Le Bras.
讲师
日期
2026年09月16日 至 2027年01月06日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:05 | Qiuzhen | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Basic graduate-level commutative algebra / algebraic geometry
课程大纲
1. Finite flat groups schemes and $p$-divisible groups (Oort, Tate)
2. Classical Dieudonné theory over perfect field of char. $p$
3. Crystalline sites and Dieudonné crystals of abelian schemes (Berthelot-Breen-Messing)
4. Dieudonné theory over perfect valuation ring of char. $p$ (Berthelot) and its generalization to perfect ring of char. $p$
5. Dieudonné theory over $\mathcal{O}_C$ (Scholze-Weinstein)
6. Overview of prisms and prismatic site
7. Prismatic Dieudonné theory (Anschütz-Le Bras)
2. Classical Dieudonné theory over perfect field of char. $p$
3. Crystalline sites and Dieudonné crystals of abelian schemes (Berthelot-Breen-Messing)
4. Dieudonné theory over perfect valuation ring of char. $p$ (Berthelot) and its generalization to perfect ring of char. $p$
5. Dieudonné theory over $\mathcal{O}_C$ (Scholze-Weinstein)
6. Overview of prisms and prismatic site
7. Prismatic Dieudonné theory (Anschütz-Le Bras)
参考资料
1. Oort ``Commutative group schemes"
2. Tate ``$p$-divisible groups"
3. Fontaine ``Groupes $p$-divisibles sur les corps locaux"
4. Berthelot-Breen-Messing ``Théorie de Dieudonné cristalline II"
5. Berthelot ``Théorie de Dieudonné sur un anneau de valuation parfait"
6. Fargues ``Groupes analytiques rigides $p$-divisibles"
7. Scholze-Weinstein ``Moduli of $p$-divisible groups"
8. Anschütz-Le Bras ``Prismatic Dieudonné theory"
2. Tate ``$p$-divisible groups"
3. Fontaine ``Groupes $p$-divisibles sur les corps locaux"
4. Berthelot-Breen-Messing ``Théorie de Dieudonné cristalline II"
5. Berthelot ``Théorie de Dieudonné sur un anneau de valuation parfait"
6. Fargues ``Groupes analytiques rigides $p$-divisibles"
7. Scholze-Weinstein ``Moduli of $p$-divisible groups"
8. Anschütz-Le Bras ``Prismatic Dieudonné theory"
听众
Advanced Undergraduate
, Graduate
, 博士后
视频公开
不公开
笔记公开
公开
语言
英文
讲师介绍
Yong Suk Moon于2022年秋作为助理研究员入职BIMSA。他的研究方向包括数论和算术几何。具体而言，他现在的研究集中在p-进霍奇理论，Fontaine-Mazur猜想和p-进Langlands纲领。他于2016年在哈佛大学取得博士学位，之后在普度大学作为访问助理教授工作3年，2019-2022年在美国亚利桑那大学做博士后。