Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Toby STAFFORD - Université du Michigan,
Titre Noncommutative rational surfaces
Horaire14:00 à 15:00
RésumeOne of the major open problems in non-commutative algebraic geometry is the classification of non-commutative surfaces (or of connected graded algebras of Gelfand-Kirillov dimension 3). Artin has conjectured that the corresponding division rings are known, with the generic case being the ring of fractions of the so-called Sklyanin algebra. In this talk we will discuss progress in classifying the non commutative surfaces birational to Proj of that algebra. In particular, non-commutative analogues +of blowing up and down are understood, and this has for example been used to determine the subalgebras of the Sklyanin algebra. This talk will survey this subject and show in particular that Van den Bergh's quadric surfaces are minimal models in a very strong sense. This is joint work with Dan Rogalski and Sue Sierra.