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 : Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :Zoom ou IHP Salle 01

Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


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.
SalleZoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
AdresseZoom ou IHP Salle 01