Moduli of objects in dg-categories
Moduli of objects in dg-categories
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DOI：
10.1016/j.ansens.2007.05.001
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发表时间：
2005-03
影响因子：
1.9
通讯作者：
B. Toën;M. Vaquié
中科院分区：
文献类型：
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作者：
B. Toën;M. Vaquié
对任意dg-范畴T（基环k上），我们定义了一个D-栈MT，在[TONN B.，VEZZOSI G.，同伦代数几何II：几何堆栈和应用，美国数学学会会员，in press]，classifying certain Top-dg-modules.当T饱和时，MT将紧凑对象分类在与T相关联的三角范畴[T]中。这项工作的主要结果表明，在T上的某些有限条件下（例如，如果它是饱和的），D-堆叠MT是局部几何的（即开放和几何子堆叠的并集）。作为结果，我们证明了饱和dg-范畴的自等价群的代数性。我们还得到了在光滑和适当的方案上完美复形的合理模的存在性，以及有限复形的表示的复形的合理模的存在性。
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 (eg if it is saturated) the D−-stack MT is locally geometric (ie 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.© 2007 Published by Elsevier Masson SAS