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• W2159924184 abstract "The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D−-stack MT in the sense of [Toën B., Vezzosi G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press], classifying certain Top-dg-modules. When T is saturated, MT classifies compact objects in the triangulated category [T] associated to T. The main result of this work states that under certain finiteness conditions on T (e.g. if it is saturated) the D−-stack MT is locally geometric (i.e. union of open and geometric sub-stacks). As a consequence we prove the algebraicity of the group of auto-equivalences of saturated dg-categories. We also obtain the existence of reasonable moduli for perfect complexes on a smooth and proper scheme, as well as complexes of representations of a finite quiver. L'objectif de ce travail est de démontrer l'existence d'un espace des modules algébrique classifiant les objets dans une catégorie triangulée donnée. Pour toute dg-catégorie T (au-dessus d'un anneau de base k), nous définissons un D−-champ MT dans le sens de [Toën B., Vezzosi G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press], qui classifie certains Top-dg-modules. Quand T est saturée, MT classifie les objets compacts dans la catégorie triangulée [T] associée à T. Le résultat principal de ce travail énonce que, sous certaines conditions de finitude sur T (par exemple si T est saturée), le D−-champ MT est localement géométrique (i.e. réunion de sous-champs ouverts géométriques). Comme conséquence, nous démontrons l'algébricité du groupe des auto-équivalences des dg-catégories saturées. Nous obtenons aussi l'existence d'un espace des modules raisonnable pour les complexes parfaits sur un schéma propre et lisse, ainsi que pour les complexes de représentations de carquois finis." @default.
• W2159924184 created "2016-06-24" @default.
• W2159924184 creator A5039846179 @default.
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• W2159924184 date "2007-05-01" @default.
• W2159924184 modified "2023-10-10" @default.
• W2159924184 title "Moduli of objects in dg-categories" @default.
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• W2159924184 doi "https://doi.org/10.1016/j.ansens.2007.05.001" @default.
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