Crystalline representations and \(F\)-crystals. (English) Zbl 1184.11052

Kisin, Mark

Ginzburg, Victor (ed.), Algebraic geometry and number theory. In Honor of Vladimir Drinfeld’s 50th birthday. Basel: Birkhäuser (ISBN 978-0-8176-4471-0/hbk). Progress in Mathematics 253, 457-496 (2006).

Summary: Following ideas of Berger and Breuil, we give a new classification of crystalline representations. The objects involved may be viewed as local, characteristic 0 analogues of the “shtukas” introduced by Drinfeld. We apply our results to give a classification of \(p\)-divisible groups and finite flat group schemes, conjectured by Breuil, and to show that a crystalline representation with Hodge-Tate weights \(0, 1\) arises from a \(p\)-divisible group, a result conjectured by Fontaine.
For the entire collection see [Zbl 1113.00007].

MSC:

11S20	Galois theory
14F30	\(p\)-adic cohomology, crystalline cohomology

Keywords:

classification of crystalline representations; classification of \(p\)-divisible groups; finite flat group schemes; crystalline representation with Hodge-Tate weights