Relative nonhomogeneous Koszul duality [electronic resource] / Leonid Positselski.

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Relative nonhomogeneous Koszul duality [electronic resource] / Leonid Positselski.

9783030895402 (electronic bk.)
3030895408 (electronic bk.)
3030895394
9783030895396

Cham, Switzerland : Birkhäuser, 2022.

English

1 online resource.

10.1007/978-3-030-89540-2 doi

QA564

512/.46

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 PoincareBirkhoffWitt 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 time in 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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed February 25, 2022).

Frontiers in mathematics.

Print version: 9783030895396

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