Leonid Positselski - Böcker
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6 produkter
6 produkter
591 kr
Skickas inom 10-15 vardagar
This research monograph develops the theory of relative nonhomogeneous Koszul duality. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry.
Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes
Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product
Inbunden, Engelska, 2023
1 275 kr
Skickas inom 7-10 vardagar
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.
Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes
Quasi-Coherent Torsion Sheaves, the Semiderived Category, and the Semitensor Product
Häftad, Engelska, 2024
1 275 kr
Skickas inom 10-15 vardagar
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.
2 449 kr
Kommande
The subject of this monograph lies on the border of algebraic geometry with modern homological algebra. A scheme (in the sense of Grothendieck) is a basic notion in contemporary algebraic geometry, while other basic notions involved (cotorsion modules, and more generally complete cotorsion pairs) are fundamental to homological ring and module theory of the last quarter century. Contraherent cosheaves have been previously introduced by the author and are further presented and developed in this book.
Homological Algebra of Semimodules and Semicontramodules
Semi-infinite Homological Algebra of Associative Algebraic Structures
Inbunden, Engelska, 2010
538 kr
Skickas inom 10-15 vardagar
ThesubjectofthisbookisSemi-In?niteAlgebra,ormorespeci?cally,Semi-In?nite Homological Algebra. The term "semi-in?nite" is loosely associated with objects that can be viewed as extending in both a "positive" and a "negative" direction, withsomenaturalpositioninbetween,perhapsde?nedupto a"?nite"movement. Geometrically, this would mean an in?nite-dimensional variety with a natural class of "semi-in?nite" cycles or subvarieties, having always a ?nite codimension in each other, but in?nite dimension and codimension in the whole variety [37]. (For further instances of semi-in?nite mathematics see, e. g. , [38] and [57], and references below. ) Examples of algebraic objects of the semi-in?nite type range from certain in?nite-dimensional Lie algebras to locally compact totally disconnected topolo- cal groups to ind-schemes of ind-in?nite type to discrete valuation ?elds. From an abstract point of view, these are ind-pro-objects in various categories, often - dowed with additional structures. One contribution we make in this monograph is the demonstration of another class of algebraic objects that should be thought of as "semi-in?nite", even though they do not at ?rst glance look quite similar to the ones in the above list.These are semialgebras over coalgebras, or more generally over corings - the associative algebraic structures of semi-in?nite nature. The subject lies on the border of Homological Algebra with Representation Theory, and the introduction of semialgebras into it provides an additional link with the theory of corings [23], as the semialgebrasare the natural objects dual to corings.
Homological Algebra of Semimodules and Semicontramodules
Semi-infinite Homological Algebra of Associative Algebraic Structures
Häftad, Engelska, 2012
538 kr
Skickas inom 10-15 vardagar
ThesubjectofthisbookisSemi-In?niteAlgebra,ormorespeci?cally,Semi-In?nite Homological Algebra. The term "semi-in?nite" is loosely associated with objects that can be viewed as extending in both a "positive" and a "negative" direction, withsomenaturalpositioninbetween,perhapsde?nedupto a"?nite"movement. Geometrically, this would mean an in?nite-dimensional variety with a natural class of "semi-in?nite" cycles or subvarieties, having always a ?nite codimension in each other, but in?nite dimension and codimension in the whole variety [37]. (For further instances of semi-in?nite mathematics see, e. g. , [38] and [57], and references below. ) Examples of algebraic objects of the semi-in?nite type range from certain in?nite-dimensional Lie algebras to locally compact totally disconnected topolo- cal groups to ind-schemes of ind-in?nite type to discrete valuation ?elds. From an abstract point of view, these are ind-pro-objects in various categories, often - dowed with additional structures. One contribution we make in this monograph is the demonstration of another class of algebraic objects that should be thought of as "semi-in?nite", even though they do not at ?rst glance look quite similar to the ones in the above list.These are semialgebras over coalgebras, or more generally over corings - the associative algebraic structures of semi-in?nite nature. The subject lies on the border of Homological Algebra with Representation Theory, and the introduction of semialgebras into it provides an additional link with the theory of corings [23], as the semialgebrasare the natural objects dual to corings.