LEADER 03509nam 22005415 450 001 9910544846603321 005 20240215145033.0 010 $a9783030895402$b(electronic bk.) 010 $z9783030895396 024 7 $a10.1007/978-3-030-89540-2 035 $a(MiAaPQ)EBC6886997 035 $a(Au-PeEL)EBL6886997 035 $a(CKB)21167559800041 035 $a(DE-He213)978-3-030-89540-2 035 $a(PPN)260825557 035 $a(EXLCZ)9921167559800041 100 $a20220210d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRelative Nonhomogeneous Koszul Duality /$fby Leonid Positselski 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (303 pages) 225 1 $aFrontiers in Mathematics,$x1660-8054 311 08$aPrint version: Positselski, Leonid Relative Nonhomogeneous Koszul Duality Cham : Springer International Publishing AG,c2022 9783030895396 320 $aIncludes bibliographical references. 327 $aPreface -- Prologue -- Introduction -- Homogeneous Quadratic Duality over a Base Ring -- Flat and Finitely Projective Koszulity -- Relative Nonhomogeneous Quadratic Duality -- The Poincare-Birkhoff-Witt Theorem -- Comodules and Contramodules over Graded Rings -- Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side -- Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side -- The Co-Contra Correspondence -- Koszul Duality and Conversion Functor -- Examples -- References. 330 $aThis research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare?Birkhoff?Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail. 410 0$aFrontiers in Mathematics,$x1660-8054 606 $aAlgebra, Homological 606 $aCategory Theory, Homological Algebra 606 $aTeoria de la dualitat (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aAlgebra, Homological. 615 14$aCategory Theory, Homological Algebra. 615 7$aTeoria de la dualitat (Matemātica) 676 $a515.782 676 $a512.46 700 $aPositselski$b Leonid$f1973-$0499475 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910544846603321 996 $aRelative Nonhomogeneous Koszul Duality$92644851 997 $aUNINA