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) Amnon YEKUTIELI - Ben Gurion University, Israel et Université Paris 7,
Titre Duality and Tilting for Commutative DG Rings
Horaire14:00 à 15:00
RésumeWe study super-commutative nonpositive DG rings. An example is the Koszul complex associated to a sequence of elements in a commutative ring. More generally such DG rings arise as semi-free resolutions of rings. They are also the affine DG schemes in derived algebraic geometry. The theme of this talk is that in many ways a DG ring $A$ resembles an infinitesimal extension, in the category of rings, of the ring $H^0(A)$. I first discuss localization of DG rings on $Spec(H^0(A))$ and the cohomological noetherian property. Then I introduce perfect, tilting and dualizing DG $A$-modules. Existence of dualizing DG modules is proved under quite general assumptions. The derived Picard group $DPic(A)$ of $A$, whose objects are the tilting DG modules, classifies dualizing DG modules. It turns out that $DPic(A)$ is canonically isomorphic to $DPic(H^0(A))$, and that latter group is known by earlier work. A consequence is that $A$ and $H^0(A)$ have the same (isomorphism classes of) dualizing DG modules.