Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes: Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00576365" target="_blank" >RIV/67985840:_____/23:00576365 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/978-3-031-37905-5" target="_blank" >http://dx.doi.org/10.1007/978-3-031-37905-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-37905-5" target="_blank" >10.1007/978-3-031-37905-5</a>

Result language

angličtina

Original language name

Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes: Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product

Original language description

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.

Czech name

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Czech description

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Type

B - Specialist book

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-3-031-37904-8

Number of pages

216

Publisher name

Birkhäuser

Place of publication

Cham

UT code for WoS book

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