Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes

Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes
Author :
Publisher : Springer Nature
Total Pages : 225
Release :
ISBN-10 : 9783031379055
ISBN-13 : 3031379055
Rating : 4/5 (055 Downloads)

Book Synopsis Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes by : Leonid Positselski

Download or read book Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes written by Leonid Positselski and published by Springer Nature. This book was released on 2023-10-16 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes Related Books

Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes
Language: en
Pages: 225
Authors: Leonid Positselski
Categories: Mathematics
Type: BOOK - Published: 2023-10-16 - Publisher: Springer Nature

GET EBOOK

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 a
Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes
Language: en
Pages: 0
Authors: Leonid Positselski
Categories: Mathematics
Type: BOOK - Published: 2023-09-26 - Publisher: Birkhäuser

GET EBOOK

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 a
Representation Theory and Algebraic Geometry
Language: en
Pages: 458
Authors: Vladimir Baranovsky
Categories: Mathematics
Type: BOOK - Published: 2022-06-15 - Publisher: Springer Nature

GET EBOOK

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pio
Fundamental Algebraic Geometry
Language: en
Pages: 354
Authors: Barbara Fantechi
Categories: Mathematics
Type: BOOK - Published: 2005 - Publisher: American Mathematical Soc.

GET EBOOK

Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence
Coherent Analytic Sheaves
Language: en
Pages: 267
Authors: H. Grauert
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

... Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem