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arXiv · 1507.05509

Uniqueness of dg enhancements for the derived category of a Grothendieck category

Alberto Canonaco·Paolo Stellari
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Abstract

We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. Under some additional assumptions, we show that the same result holds true for its subcategory of compact objects. As a consequence, we deduce that the unbounded derived category of quasi-coherent sheaves on an algebraic stack and the category of perfect complexes on a noetherian concentrated algebraic stack with quasi-finite affine diagonal and enough perfect coherent sheaves have a unique dg enhancement. In particular, the category of perfect complexes on a noetherian scheme with enough locally free sheaves has a unique dg enhancement.

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Alberto Canonaco, Paolo Stellari. 2015-07-20. Uniqueness of dg enhancements for the derived category of a Grothendieck category. https://arxiv.org/abs/1507.05509

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