Pré-Publication, Document De Travail Année : 2005

Moduli of objects in dg-categories

Résumé

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ 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 $\mathcal{M}_{T}$ 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 a saturated dg-category. 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.

Dates et versions

hal-00022949 , version 1 (16-04-2006)

Identifiants

Citer

B. Toen, Michel Vaquié. Moduli of objects in dg-categories. 2005. ⟨hal-00022949⟩
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