Travaux de Zink
Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque no. 311  (2007), Talk no. 964, p. 341-364

The diverse Dieudonné theories have as their common goal the classification of formal groups and p-divisible groups. The most recent theory is Zink’s theory of displays. A display over a ring R is a finitely generated projective module over the ring of Witt vectors, W(R), equipped with additional structures. Zink has shown that using this notion, more concrete than those previously defined, one can obtain a good theory and prove an equivalence theorem in great generality. I will give an overview of his theory as well as sketch several proofs.

Les diverses théories de Dieudonné ont toutes pour but de classifier les groupes formels et les groupes p-divisibles. La plus récente est la théorie des étalages (displays) de Zink. Un étalage sur un anneau R est un module projectif de type fini sur l’anneau des vecteurs de Witt, W(R), muni de structures supplémentaires. Zink a montré qu’à l’aide de cette notion, plus concrète que celles utilisées antérieurement, on peut obtenir une bonne théorie et démontrer des théorèmes d’équivalence dans des cas assez généraux. On donnera une vue d’ensemble de sa théorie ainsi que quelques idées des démonstrations.

Classification:  14F30,  14L05
Keywords: cristaux de Dieudonné, étalages, groupes formels, groupes p-divisibles
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Messing, William. Travaux de Zink, in Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Talk no. 964, pp. 341-364. http://www.numdam.org/item/SB_2005-2006__48__341_0/

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