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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 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Semi-infinite algebraic geometry of quasi-coherent sheaves on Ind-schemes/ by Leonid Positselski.
其他題名:	quasi-coherent torsion sheaves, the semiderived category, and the semitensor product /
作者:	Positselski, Leonid.
出版者:	Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:	xix, 216 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
電子資源:	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:

678397
Category Theory, Homological Algebra.

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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