 Invariance Under Postcomposition with a Smooth MorphismLeonid Positselski
Chapter Chapter 10 in Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes, 2023, pp 157-177 from Springer Abstract: Abstract Let π $${\mathfrak X}$$ be an ind-semi-separated ind-Noetherian ind-scheme, and let Ο : π β² β π $$\tau \colon {\mathfrak X}'\longrightarrow {\mathfrak X}$$ be a smooth affine morphism of finite type. Let Ο β² : π β π β² $$\pi '\colon {\boldsymbol {\mathfrak Y}}\longrightarrow {\mathfrak X}'$$ be a flat affine morphism, and let Ο : π β π $$\pi \colon {\boldsymbol {\mathfrak Y}}\longrightarrow {\mathfrak X}$$ denote the composition Ο = Ο Ο β² $$\pi =\tau \pi '$$ . Let D β’ $${\mathcal D}^{\scriptstyle \bullet }$$ be a dualizing complex on π $${\mathfrak X}$$ ; then D β² β’ = Ο β D β’ $${\mathcal D}'{ }^{\scriptstyle \bullet }= \tau ^*{\mathcal D}^{\scriptstyle \bullet }$$ is a dualizing complex on π β² $${\mathfrak X}'$$ . The aim of this chapter is to show that the constructions of Chaps. 7β8, including the semiderived category of quasi-coherent torsion sheaves on π $${\boldsymbol {\mathfrak Y}}$$ and the semitensor product operation on it, are preserved by the passage from the flat affine moprhism Ο β² $$\pi '$$ to the flat affine morphism Ο $$\pi $$ . Date: 2023 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-37905-5_10 Ordering information: This item can be ordered from DOI: 10.1007/978-3-031-37905-5_10 Access Statistics for this chapter More chapters in Springer Books from Springer |
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