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Semi-infinite algebraic geometry of ...

Positselski, Leonid.

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Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes = quasi-coherent torsion sheaves, the semiderived category, and the semitensor product /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes/ by Leonid Positselski.
Reminder of title:	quasi-coherent torsion sheaves, the semiderived category, and the semitensor product /
Author:	Positselski, Leonid.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xix, 216 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Algebraic. -
Online resource:	https://doi.org/10.1007/978-3-031-37905-5
ISBN:	9783031379055

Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes = quasi-coherent torsion sheaves, the semiderived category, and the semitensor product /
Positselski, Leonid.

Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemesquasi-coherent torsion sheaves, the semiderived category, and the semitensor product /[electronic resource] :by Leonid Positselski. - Cham :Springer Nature Switzerland :2023. - xix, 216 p. :ill., digital ;24 cm.

Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.

ISBN: 9783031379055

Standard No.: 10.1007/978-3-031-37905-5doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes = quasi-coherent torsion sheaves, the semiderived category, and the semitensor product /
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245 1 0 $a Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes $h [electronic resource] : $b quasi-coherent torsion sheaves, the semiderived category, and the semitensor product / $c by Leonid Positselski.
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300 $a xix, 216 p. : $b ill., digital ; $c 24 cm.
520 $a Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.
650 0 $a Geometry, Algebraic. $3 532048
650 0 $a Sheaf theory. $3 612610
650 1 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Category Theory, Homological Algebra. $3 899944
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