Groupes pdivisibles, groupes finis et modules filtrés
Abstract
Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified pdivisibles groups and finite flat pgroups 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 HodgeTate weights in {0,1} contains as a lattice the Tate module of a pdivisible group over A.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2000
 arXiv:
 arXiv:math/0009252
 Bibcode:
 2000math......9252B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 61 pages, French, published version