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

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
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