Séminaires : Séminaire Théorie des Nombres

Equipe(s) : fa, tn, tga,
Responsables :Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel
Email des responsables : cathy.swaenepoel@imj-prg.fr
Salle :
Adresse :



Orateur(s) R. Pink - ,
Titre Inseparable field extensions associated to $p$-divisible groups
Horaire14:00 à 16:00
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.