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Relative Nonhomogeneous Koszul Duality 1st Edition by Leonid Positselski ISBN 978-3030895396 3030895394

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Relative Nonhomogeneous Koszul Duality 1st ed. 2021 Edition Leonid Positselski Digital Instant Download

Author(s): Leonid Positselski
ISBN(s): 9783030895396, 3030895394
Edition: 1st ed. 2021
File Details: PDF, 2.38 MB
Year: 2022
Language: english
SKU: EB-51157750 Category: Tag:

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Product details: 

ISBN 10:  3030895394

ISBN 13: 978-3030895396

Author:  Leonid Positselski

This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research.

This book, written by one of the world’s leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare–Birkhoff–Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. 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. For the first timein the history of Koszul duality the derived D-Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.

Table of contents: 

  1. Preface

  2. Prologue

  3. Introduction

  4. Homogeneous Quadratic Duality over a Base Ring

  5. Flat and Finitely Projective Koszulity

  6. Relative Nonhomogeneous Quadratic Duality

  7. The Poincaré–Birkhoff–Witt Theorem

  8. Comodules and Contramodules over Graded Rings

  9. Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side

  10. Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side

  11. The Co-Contra Correspondence

  12. Koszul Duality and Conversion Functor

  13. Examples

  14. References

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Tags: Leonid Positselski, Relative Nonhomogeneous, Koszul Duality