Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) R. Pink - ,
Titre Inseparable field extensions associated to $p$-divisible groups
Date14/02/2005
Horaire14:00 à 16:00
Diffusion
RésumeLet $X$ be a $p$-divisible group over a field $K$ ofcharacteristic $p>0$. Then the field of definition $K(x)$ of any point$x\in X$ is a finite extension of~$K$, which may be separable orinseparable. How do the separable and inseparable degrees of $K(x)/K$vary with $x$? The separable degree is determined by the action of theabsolute Galois group of $K$ on the Tate module of~$X$, and hence bygroup theory. In a joint project by Frans Oort and the speaker, apartial answer is given for the inseparable degree. One of the toolsused is deformation theory of $p$-divisible groups. Another is thetheory of multilinear morphisms for commutative group schemes and$p$-divisible groups, which incorporates tensor product and inner hom,and which allows the extension of the results to a variety of similarquestions.
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