LEADER 04859nam 22007695 450 001 9910136809303321 005 20230706144416.0 010 $a3-319-26437-0 024 7 $a10.1007/978-3-319-26437-0 035 $a(CKB)3710000000627458 035 $a(SSID)ssj0001659562 035 $a(PQKBManifestationID)16438299 035 $a(PQKBTitleCode)TC0001659562 035 $a(PQKBWorkID)14989312 035 $a(PQKB)10300760 035 $a(DE-He213)978-3-319-26437-0 035 $a(MiAaPQ)EBC6287667 035 $a(MiAaPQ)EBC5591473 035 $a(Au-PeEL)EBL5591473 035 $a(OCoLC)944445429 035 $a(PPN)192290177 035 $a(EXLCZ)993710000000627458 100 $a20160308d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMinimal Free Resolutions over Complete Intersections /$fby David Eisenbud, Irena Peeva 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (X, 107 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2152 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-26436-2 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Acknowledgments -- Contents -- 1 Introduction and Survey -- 1.1 How We Got Here -- Revealing the Pattern -- 1.2 What is a Higher Matrix Factorization? -- Matrix Factorizations of a Sequence of Elements -- 1.3 What's in This Book? -- High Syzygies are Higher Matrix Factorization Modules -- Minimal R-Free and S-Free Resolutions -- Syzygies over Intermediate Quotient Rings -- 1.4 Notation and Conventions -- 2 Matrix Factorizations of One Element -- 2.1 Matrix Factorizations and Resolutions over a Hypersurface -- 3 Finite Resolutions of HMF Modules -- 3.1 The Minimal S-Free Resolution of a Higher Matrix Factorization Module -- 3.2 Consequences -- 3.3 Building a Koszul Extension -- 3.4 Higher Homotopies -- 4 CI Operators -- 4.1 CI Operators -- 4.2 The Action of the CI Operators on Ext -- 4.3 Resolutions with a Surjective CI Operator -- 5 Infinite Resolutions of HMF Modules -- 5.1 The Minimal R-Free Resolution of a Higher Matrix Factorization Module -- 5.2 Betti Numbers -- 5.3 Strong Matrix Factorizations -- 5.4 Resolutions over Intermediate Rings -- 6 Far-Out Syzygies -- 6.1 Pre-stable Syzygies and Generic CI Operators -- 6.2 The Graded Case -- 6.3 The Box Complex -- 6.4 From Syzygies to Higher Matrix Factorizations -- 6.5 Betti Numbers of Pre-stable Matrix Factorizations -- 7 The Gorenstein Case -- 7.1 Syzygies and Maximal Cohen-Macaulay Modules -- 7.2 Stable Syzygies in the Gorenstein Case -- 7.3 Maximal Cohen-Macaulay Approximations -- 7.4 Stable Matrix Factorizations over a Gorenstein Ring -- 8 Functoriality -- 8.1 HMF Morphisms -- References -- Index. 330 $aThis book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2152 606 $aCommutative algebra 606 $aCommutative rings 606 $aGeometry, Algebraic 606 $aAlgebra, Homological 606 $aMathematical physics 606 $aCommutative Rings and Algebras 606 $aAlgebraic Geometry 606 $aCategory Theory, Homological Algebra 606 $aTheoretical, Mathematical and Computational Physics 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aGeometry, Algebraic. 615 0$aAlgebra, Homological. 615 0$aMathematical physics. 615 14$aCommutative Rings and Algebras. 615 24$aAlgebraic Geometry. 615 24$aCategory Theory, Homological Algebra. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a512.62 700 $aEisenbud$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$057349 702 $aPeeva$b Irena$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910136809303321 996 $aMinimal Free Resolutions over Complete Intersections$92182309 997 $aUNINA