---

＜電子ブック＞
Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes : Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product / by Leonid Positselski

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2023
本文言語	英語
大きさ	XIX, 216 p : online resource
著者標目	*Positselski, Leonid author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebra, Homological FREE:Algebraic Geometry FREE:Commutative Rings and Algebras FREE:Category Theory, Homological Algebra
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-37905-5

 類似資料