 Ind-Schemes of Ind-Finite Type and the ! $$!$$ -Tensor ProductLeonid Positselski
Chapter Chapter 6 in Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes, 2023, pp 81-103 from Springer Abstract: Abstract Throughout this chapter, π $$\Bbbk $$ denotes a fixed ground field. Given two ind-schemes π β² $${\mathfrak X}'$$ and π β³ $${\mathfrak X}''$$ (or two schemes X β² $$X'$$ and X β³ $$X''$$ ) over π $$\Bbbk $$ , we denote the fibered product π β² Γ Spec π π β³ $${\mathfrak X}'\times _{ \operatorname {\mathrm {Spec}}\Bbbk }{\mathfrak X}''$$ (or X β² Γ Spec π X β³ $$X'\times _{ \operatorname {\mathrm {Spec}}\Bbbk }X''$$ ) simply by π β² Γ π π β³ $${\mathfrak X}'\times _\Bbbk {\mathfrak X}''$$ (or X β² Γ π X β³ $$X'\times _\Bbbk X''$$ ) for brevity. (See Sects. 1.1 and 1.2 for a discussion of fibered products of ind-schemes.) Let π $$\mathfrak {X}$$ be an ind-separated ind-scheme of ind-finite type over the field π $$\Bbb {k}$$ . The aim of this chapter is to describe the cotensor product functor, for a suitable choice of the dualizing complex on π $$\mathfrak {X}$$ , as the derived !-restriction to the diagonal of the external tensor product on π Γ k π $$\mathfrak {X}\times _k\mathfrak {X}$$ of two given complexes of quasi-coherent sheaves on π $$\mathfrak {X}$$ . 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_6 Ordering information: This item can be ordered from DOI: 10.1007/978-3-031-37905-5_6 Access Statistics for this chapter More chapters in Springer Books from Springer |
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