Completion, čech and local homology and cohomology : interactions between them /: interactions between them. ([2018])

• Record Type: Book
• Further Information: Note: Peter Schenzel, Anne-Marie Simon.
• Authors: Schenzel, Peter; Simon, Anne-Marie
• Contents: Intro; Introduction; Contents; Part I Modules; 1 Preliminaries and Auxiliary Results; 1.1 Complexes; 1.2 Inverse Limits; 1.3 Direct Limits; 1.4 Ext-Tor Duality and General Matlis Duality; 1.5 Cones and Fibers; 2 Adic Topology and Completion; 2.1 Topological Preliminaries; 2.2 The Case of Finitely Generated Ideals; 2.3 Noetherian Rings and Matlis Duality; 2.4 Completions of Flat Modules over a Noetherian Ring; 2.5 The Left-Derived Functors of Completion; 2.6 Relative Flatness and Completion in the General Case; 2.7 Relatively Injective and Torsion Modules; 2.8 Some Examples 3 Ext-Tor Vanishing and Completeness Criteria3.1 Completeness and Pseudo-completeness Criteria; 3.2 Modules of Infinite Co-depth; 3.3 When is a Finitely Generated Module Complete?; 3.4 Ext-Depth and Tor-Codepth with Local (Co-)Homology; Part II Complexes; 4 Homological Preliminaries; 4.1 Double Complexes and Truncations; 4.2 The Microscope; 4.3 The Telescope; 4.4 Special Resolutions and Their Uses; 4.5 Minimal Injective Resolutions for Unbounded Complexes; 4.6 Ext and Tor with Inverse and Direct Limits; 5 Koszul Complexes, Depth and Codepth; 5.1 Ext-Depth and Tor-Codepth 5.2 Basics About Koszul Complexes5.3 The Ext-Depth Tor-Codepth Sensitivity of the Koszul Complex; 5.4 Koszul Homology of Modules; 6 Čech Complexes, Čech Homology and Cohomology; 6.1 The Čech Complex; 6.2 A Free Resolution of the Čech Complex; 6.3 Čech Homology and Cohomology; 6.4 Some Classes Related to the Čech Complex; 6.5 Composites; 6.6 Depth, Codepth and Čech Complexes; 7 Local Cohomology and Local Homology; 7.1 The General Case; 7.2 First Vanishing Results with Applications to the Class mathcalTmathfraka; 7.3 Weakly Pro-regular Sequences; 7.4 Local and Čech Cohomology with Telescope 7.5 Local and Čech Homology with Microscope7.6 Depth and Codepth with Local (Co-)Homology; 8 The Formal Power Series Koszul Complex; 8.1 Čech Homology and Koszul Complexes; 8.2 Applications to Weakly Pro-regular Sequences; 8.3 Applications to Koszul Homology; 8.4 The Case of a Single Element; 9 Complements and Applications; 9.1 Composites; 9.2 Adjointness and Duality; 9.3 Some Endomorphisms; 9.4 Mayer-Vietoris Sequences for Local and Čech (Co-)Homology; 9.5 On the use of the classes mathcalCmathfraka and mathcalBmathfraka; 9.6 Homologically Complete and Cohomologically Torsion Complexes 9.7 Homological Completeness and Cosupport9.8 Change of Rings; Part III Duality; 10 Čech and Local Duality; 10.1 Bounded Injective Complexes with Finitely Generated Cohomology; 10.2 Čech Cohomology and Duality; 10.3 Canonical Modules; 10.4 Local Duality over Cohen-Macaulay Local Rings; 10.5 On Gorenstein Local Rings and Duality; 10.6 Local Cohomology over Finite Local Gorenstein Algebras; 11 Dualizing Complexes; 11.1 Evaluation Morphisms of Complexes; 11.2 Definition of Dualizing Complexes for Noetherian Rings; 11.3 First Change of Rings; 11.4 Characterization and Uniqueness
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 512.4; Mathematics; Commutative algebra; Homology theory; Algebra; MATHEMATICS / Algebra / Intermediate; Mathematics -- Algebra -- Abstract; Algebra; Electronic books
• Languages: English
• ISBNs: 9783319965178; 3319965174
• Related ISBNs: 9783319965161
• Notes: Note: Includes bibliographical references and indexes.; Note: Online resource; title from PDF title page (EBSCO, viewed September 19, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.