دانلود کتاب Progress in Commutative Algebra 1: Combinatorics and Homology

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Preface\nBoij-Söderberg Theory: Introduction and Survey\n 1 The Boij-Söderberg Conjectures\n 1.1 Resolutions and Betti Diagrams\n 1.2 The Positive Cone of Betti Diagrams\n 1.3 Herzog-Kühl Equations\n 1.4 Pure resolutions\n 1.5 Linear Combinations of Pure Diagrams\n 1.6 The Boij-Söderberg Conjectures\n 1.7 Algorithmic Interpretation\n 1.8 Geometric Interpretation\n 2 The Exterior Facets of the Boij-Söderberg Fan and Their Supporting Hyperplanes\n 2.1 The Exterior Facets\n 2.2 The Supporting Hyperplanes\n 2.3 Pairings of Vector Bundles and Resolutions\n 3 The Existence of Pure Free Resolutions and of Vector Bundles with Supernatural Cohomology\n 3.1 The Equivariant Pure Free Resolution\n 3.2 Equivariant Supernatural Bundles\n 3.3 Characteristic Free Supernatural Bundles\n 3.4 The Characteristic Free Pure Resolutions\n 3.5 Pure Resolutions Constructed from Generic Matrices\n 4 Cohomology of Vector Bundles on Projective Spaces\n 4.1 Cohomology Tables\n 4.2 The Fan of Cohomology Tables of Vector Bundles\n 4.3 Facet Equations\n 5 Extensions to Non-Cohen-Macaulay Modules and to Coherent Sheaves\n 5.1 Betti Diagrams of Graded Modules in General\n 5.2 Cohomology of Coherent Sheaves\n 6 Further Topics\n 6.1 The Semigroup of Betti Diagrams of Modules\n 6.2 Variations on the Grading\n 6.3 Poset Structures\n 6.4 Computer Packages\n 6.5 Three Basic Problems\nHilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way\n 1 Introduction\n 2 Approach I: Nine Double Points\n 3 Approach I: Points on Cubics\n 4 Approach II: Points on Cubics\nEdge Ideals: Algebraic and Combinatorial Properties\n 1 Introduction\n 2 Algebraic and Combinatorial Properties of Edge Ideals\n 3 Invariants of Edge Ideals: Regularity, Projective Dimension, Depth\n 4 Stability of Associated Primes\nThree Simplicial Resolutions\n 1 Introduction\n 2 Background and Notation\n 2.1 Algebra\n 2.2 Combinatorics\n 3 The Taylor Resolution\n 4 Simplicial Resolutions\n 5 The Scarf Complex\n 6 The Lyubeznik Resolutions\n 7 Intersections\n 8 Questions\nA Minimal Poset Resolution of Stable Ideals\n 1 Introduction\n 2 Poset Resolutions and Stable Ideals\n 3 The Shellability of PN\n 4 The topology of PN and properties of D (PN)\n 5 Proof of Theorem 2.4\n 6 A Minimal Cellular Resolution of R/N\nSubsets of Complete Intersections and the EGH Conjecture\n 1 Introduction\n 2 Preliminary Definitions and Results\n 2.1 The Eisenbud-Green-Harris Conjecture and Complete Intersections\n 2.2 Some Enumeration\n 3 Rectangular Complete Intersections\n 4 Some Key Tools\n 4.1 Pairs of Hilbert Functions and Maximal Growth\n 4.2 Ideals Containing Regular Sequences\n 5 Subsets of Complete Intersections in ℙ2\n 6 Subsets of C.I. (2, d2,d3) with d2 = d3\n 7 Subsets of C.I. (3, d2, d3) with d3 = d2\n 8 An Application: The Cayley-Bacharach Property\nThe Homological Conjectures\n 1 Introduction\n 2 The Serre Multiplicity Conjectures\n 2.1 The Vanishing Conjecture\n 2.2 Gabber’s Proof of the Nonnegativity Conjecture\n 2.3 The Positivity Conjecture\n 3 The Peskine-Szpiro Intersection Conjecture\n 3.1 Hochsterzs Metatheorem\n 4 Generalizations of the Multiplicity Conjectures\n 4.1 The Graded Case\n 4.2 The Generalized Rigidity Conjecture\n 5 The Monomial, Direct Summand, and Canonical Element Conjectures\n 6 Cohen-Macaulay Modules and Algebras\n 6.1 Weakly Functorial Big Cohen-Macaulay Algebras\n 7 The Syzygy Conjecture and the Improved New Intersection Conjecture\n 8 Tight Closure Theory\n 9 The Strong Direct Summand Conjecture\n 10 Almost Cohen-Macaulay Algebras\n 11 A Summary of Open Questions\n 11.1 The Serre Positivity Conjecture\n 11.2 Partial Euler Characteristics\n 11.3 Strong Multiplicity Conjectures\n 11.4 Cohen-Macaulay Modules and Related Conjectures\n 11.5 Almost Cohen-Macaulay Algebras\nThe Compatibility, Independence, and Linear Growth Properties\n 1 Introduction\n 2 Primary decomposition\n 3 Compatibility of Primary Components\n 4 Maximal Primary Components, Independence\n 5 Linear growth of primary components\n 6 Linear Growth of {TorRc (M/ImM, N/JnN)}\n 7 Secondary Representation\n 8 Compatibility of Secondary Components\n 9 Applying a Result of Sharp on Artinian Modules\n 10 Independence\n 11 Minimal Secondary Components\n 12 Linear Growth of Secondary Components\nRecent Progress in Coherent Rings: a Homological Perspective\n 1 Introduction\n 2 Coherent Rings and Grade\n 2.1 Coherent Rings and (FP)R∞ Modules\n 2.2 Non-Noetherian Grade\n 3 Cohen-Macaulay Rings\n 4 Gorenstein Dimensions and the Auslander-Bridger Property\n 4.1 Gorenstein Dimensions\n 4.2 The Auslander-Bridger Formula\n 5 Gorenstein Rings and Injective Dimensions\n 6 Foundations for Coherent Complete Intersections\nNon-commutative Crepant Resolutions: Scenes from Categorical Geometry\n 1 Introduction\n 2 Morita Equivalence\n 3 (Quasi)coherent Sheaves\n 4 Derived Categories of Modules\n 5 Derived Categories of Sheaves\n 6 Example: Tilting on Projective Space\n 7 The Non-existence of Non-commutative Spaces\n 8 Resolutions of Singularities\n 9 The Minimal Model Program\n 10 Categorical Desingularizations\n 11 Example: the McKay Correspondence\n 12 Non-commutative Crepant Resolutions\n 13 Example: Normalization\n 14 MCM Endomorphism Rings\n 15 Global Dimension of Endomorphism Rings\n 16 Rational Singularities\n 17 Examples: Finite Representation Type\n 18 Example: the Generic Determinant\n 19 Non-commutative Blowups\n 20 Omissions and Open Questions