Séminaires : Séminaire de géométrie algébrique

Equipe(s) : tga,
Responsables :
Email des responsables :
Salle : http://www.imj-prg.fr/tga/sem-ga
Adresse :
Description

La page officielle du Séminaire

Le jeudi à 14h.
septembre-décembre ENS, janvier-mars Jussieu, avril-juin Sophie-Germain

La liste de diffusion


Orateur(s) Stefan Schröer - ,
Titre There is no Enriques surface over the integers
Date04/06/2020
Horaire14:00 à 15:00
Diffusion
Résume

Same access code. Send a mail to O. Debarre or F. Han or A. Höring to get it.

We show that there is no family of Enriques surfaces over the ring of integers. This extends non-existence results of Minkowski for families of finite étale chemes, of Tate and Ogg for families of elliptic curves, and of Abrashkin and Fontaine for families of abelian varieties and more general smooth proper schemes with certain restrictions on Hodge numbers. Our main idea is to study the local system of numerical classes of invertible sheaves. Among other things, our result also hinges on the Weil Conjectures, Lang's classification of rational elliptic surfaces in characteristic two, the theory of exceptional Enriques surfaces due to Ekedahl and Shepherd-Barron, some recent results on the base of their versal deformation, Shioda's theory of Mordell--Weil lattices, and an extensive combinatorial study for the pairwise interaction of genus-one fibrations.

 

Salle
Adressehttps://bigbluebutton.imj-prg.fr/b/fre-krm-zvk
© IMJ-PRG