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Moduli of objects in dg-categories.(English)Zbl 1140.18005

The paper begins a research about moduli spaces (or stacks) of objects in a triangulated category of geometric or algebraic origin. It proves the existence of an algebraic moduli classifying objects in a given triangulated category satisfying some finiteness conditions and having a dg-enhancement.
To any dg-category \({\mathcal T}\) (i.e., a set of objects together with complexes of morphisms between two objects, the composition preserving the linear and differential structures) a stack \(M\) is associated. This one classifies compact objects in the triangulated category associated to \({\mathcal T}\) when \({\mathcal T}\) is saturated. Under some finiteness conditions on \({\mathcal T}\), \(M\) is locally geometric.
From that the algebraicity of the group of auto-equivalences of saturated dg-categories and the existence of reasonable moduli for perfect complexes on a smooth and proper scheme are proved.

MSC:

18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18D20 Enriched categories (over closed or monoidal categories)
18E30 Derived categories, triangulated categories (MSC2010)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18D99 Categorical structures

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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