CrossRef 2018 15 sitasi

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

Alberto Canonaco Paolo Stellari

Abstrak

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.

Penulis (2)

Alberto Canonaco

Paolo Stellari

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Canonaco, A., Stellari, P. (2018). Uniqueness of dg enhancements for the derived category of a Grothendieck category. https://doi.org/10.4171/jems/820

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Informasi Jurnal

Tahun Terbit: 2018
Bahasa: en
Total Sitasi: 15×
Sumber Database: CrossRef
DOI: 10.4171/jems/820
Akses: Terbatas