Moduli of objects in dg-categories

2005/03/14 by Bertrand Toën, Toen, B., Michel Vaquié +1 · 9 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · doi:10.48550/arxiv.math/0503269

Abstract

To any dg-category T (over some base ring k), we define a D^--stack M_T in the sense of \citehagII, classifying certain T^op-dg-modules. When T is saturated, 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 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.

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