SÉMINAIRE DE THÉORIE DES NOMBRES 2003-2004
Le Vendredi à 15 heures 30 en Salle de Conférence
Organisateur :
Laurent Herr
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St. PetersbourgFinite flat group schemes over complete discrete valuation rings.
RÉSUMÉ
The talk is dedicated to finite commutative group schemes and their applications to the study of good reduction of Abelian varieties. The Cartier-Dieudonne modules for finite commutative group schemes (defined by Oort) are used. Several properties of Cartier-Oort modules are proved. In particular, the complete classification of finite commutative group schemes in terms of Cartier-Oort modules is given; the computation of $Ext1$ for group schemes is done. The main applications are the properties of the generic fiber functor and a complete answer to the question of N. Katz (given by B. Conrad in the case $e\leq p-1$). The possibilities of a further development of the theory are discussed.