Groupes $p$-divisibles, groupes finis et modules filtrés

By C. Breuil. 2000

174 citations recorded by the source corpus.

Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these classifications over an arbitrary complete discrete valuation ring A with unequal characteristic (0,p) and residue field k by using "generalized" filtered modules. In particular, there is no restriction on the ramification index. In the case k is included in \bar{F}_p (and p>2), we then use this new classification to prove that any crystalline representation of the Galois group of Frac(A) with Hodge-Tate weights in {0,1} contains as a lattice the Tate module of a p-divisible group over A.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/29456435a8eea0e94732f85d6e2321699c8bfae7

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In Discrete Mathematics and Combinatorics

  1. Tongyin Liu
  2. Xavier Caruso
  3. C. Breuil
  4. Vytautas Paškūnas
  5. M. Kisin

In Geometry and Topology

  1. Tongyin Liu
  2. Xavier Caruso
  3. C. Breuil
  4. T. Gee
  5. Peter Scholze
  6. B. Bhatt
  7. M. Kisin
  8. David Savitt

In Mathematical Physics

  1. Tongyin Liu
  2. Xavier Caruso
  3. C. Breuil
  4. T. Gee
  5. Peter Scholze
  6. B. Bhatt
  7. M. Kisin
  8. David Savitt

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