Séminaires : Géométrie et Théorie des Modèles

Equipe(s) : lm,
Responsables :Zoé Chatzidakis, Raf Cluckers, Georges Comte
Email des responsables : zoe.chatzidakis@imj-prg.fr
Salle :
Adresse :



Pour recevoir le programme par e-mail, écrivez à : zoe.chatzidakis@imj-prg.fr
Pour les personnes ne connaissant pas du tout de théorie des modèles, des notes introduisant les notions de base (formules, ensembles définissables, théorème de compacité, etc.) sont disponibles ici : https://webusers.imj-prg.fr/~zoe.chatzidakis/papiers/MTluminy.dvi/MTluminy.dvi. Ces personnes peuvent aussi consulter les premiers chapitres du livre Model Theory and Algebraic Geometry, E. Bouscaren ed., Springer Verlag, Lecture Notes in Mathematics 1696, Berlin 1998.Retour ligne automatique
Les notes de quelques-uns des exposés sont disponibles.

Orateur(s) Avraham Aizenbud - Weizman,
Titre Point-wise surjective presentations of stacks, or why I am not afraid of (infinity) stacks anymore
Horaire14:15 à 15:45
RésumeAny algebraic stack X can be represented by a groupoid object in the category of schemes: that is, a pair of schemes Ob, Mor and morphisms
source, target: Mor → Ob, inversion: Mor → Mor, composition: Mor ×_Ob Mor → Mor and identity: Ob → Mor that satisfy certain axioms. Yet this description of the stack X might be misleading.

Namely, given a field F which is not algebraically closed, we have a natural functor between the groupoid (Ob(F),Mor(F)) and the groupoid X(F). While this functor is fully faithful, it is often not essentially surjective.

In joint work with Nir Avni (in progress) we show that any algebraic groupoid has a presentation such that this functor will be essentially surjective for many fields (and under some assumptions on the stack, for any field). The results are also extended to Henselian rings.

Despite the title, the talk will be about usual stacks and not infinity-stacks, yet in some of the proofs it is more convenient to use the language of higher categories and I'll try to explain why.

No prior knowledge of infinity stacks will be assumed, but a superficial acquaintance with usual stacks will be helpful.