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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
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SYSNO ASEP 0576365 Druh ASEP B - Monografie Zařazení RIV B - Odborná monografie, kniha Název Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes: Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product Tvůrce(i) Positselski, Leonid (MU-W) SAI, ORCID, RID Vyd. údaje Cham: Birkhäuser, 2023 ISBN 978-3-031-37904-8 Poč.str. 216 s. Poč.výt. 200 Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. CH - Švýcarsko Vydání 1. Klíč. slova semi-infinite tensor ; semi-infinite algebraic geometry ; algebraic geometry Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA20-13778S GA ČR - Grantová agentura ČR Institucionální podpora MU-W - RVO:67985840 DOI 10.1007/978-3-031-37905-5 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2024
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