Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture

Bernhard Keller; Junyang Liu

doi:10.5802/crmath.541

Article de recherche - Algèbre, Théorie des représentations

Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture
[Structures Calabi–Yau sur les quotients de Drinfeld et la conjecture d’Amiot]

Bernhard Keller ¹ ; Junyang Liu ¹

¹ Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 135-142.

Résumé
Abstract

En 2009, Claire Amiot a donné une construction de structures de Calabi–Yau sur les quotients de Verdier. Nous esquissons comment la relever au cadre dg. Nous utilisons cette construction comme une étape importante dans l’ébauche de la preuve de la conjecture d’Amiot sur la structure des catégories triangulées 2-Calabi–Yau avec un objet de amas-basculant.

In 2009, Claire Amiot gave a construction of Calabi–Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of $2$ -Calabi–Yau triangulated categories with a cluster-tilting object.

Reçu le : 2023-05-17
Révisé le : 2023-07-14
Accepté le : 2023-07-16
Publié le : 2024-03-07

DOI : 10.5802/crmath.541

Classification : 18E30
Mots clés : Calabi–Yau structure, Verdier quotient, Drinfeld quotient, Amiot’s conjecture

Affiliations des auteurs :

Bernhard Keller ¹ ; Junyang Liu ¹

¹ Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Bernhard Keller and Junyang Liu},
     title = {Calabi{\textendash}Yau structures on {Drinfeld} quotients and {Amiot{\textquoteright}s} conjecture},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {135--142},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.541},
     language = {en},
}

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Bernhard Keller; Junyang Liu. Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 135-142. doi : 10.5802/crmath.541. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.541/

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