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Algebraic Geometry and Number Theory pp 459–496Cite as

Crystalline representations and F-crystals

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Part of the Progress in Mathematics book series (PM,volume 253)

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.

Keywords

  • Group Scheme
  • Full Subcategory
  • Divided Power
  • Coherent Sheaf
  • Unique Lift

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To Vladimir Drinfeld on his 50th birthday.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Mark Kisin

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  1. Mark Kisin
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Editors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Victor Ginzburg

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Kisin, M. (2006). Crystalline representations and F-crystals. In: Ginzburg, V. (eds) Algebraic Geometry and Number Theory. Progress in Mathematics, vol 253. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4532-8_7

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