Dualizing Complexes on Ind-Noetherian Ind-Schemes

Leonid Positselski
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Leonid Positselski: Czech Academy of Sciences, Institute of Mathematics

Chapter Chapter 4 in Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes, 2023, pp 43-61 from Springer

Abstract: Abstract Unlike for schemes, a dualizing complex on an ind-Noetherian ind-scheme is naturally viewed as an object of the coderived category of quasi-coherent torsion sheaves. In fact, a dualizing complex on an ind-Noetherian ind-scheme can well be acyclic. In this chapter, given a dualizing complex D • $${\mathcal D}^{\scriptstyle \bullet }$$ on an ind-semi-separated ind-Noetherian ind-scheme 𝔛 $${\mathfrak X}$$ , we construct a triangulated equivalence between the coderived category of the abelian category of quasi-coherent torsion sheaves and the derived category of the exact category of flat pro-quasi-coherent pro-sheaves on 𝔛 $${\mathfrak X}$$ .

Date: 2023
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DOI: 10.1007/978-3-031-37905-5_4

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