TOC Front Cover 2 Cohomology of Completions 5 Copyright Page 6 Dedication 7 Preface 9 Contents 31 INTRODUCTION 33 Chapter 1. Manipulating in Abelian Categories 33 Section 1: Categories 33 Section 2: Subobjects and Quotient-Objects 36 Section 3: Abelian Categories 43 Section 4: Imbedding of Abelian Categories 76 Section 5: Subquotients 88 Section 6: Left Coherent Rings 98 Section 7: Denumerable Direct Product and Denumerable Inverse Limit 112 Front Cover 2 Cohomology of Completions 5 Copyright Page 6 Dedication 7 Preface 9 Contents 31 INTRODUCTION 33 Chapter 1. Manipulating in Abelian Categories 33 Section 1: Categories 33 Section 2: Subobjects and Quotient-Objects 36 Section 3: Abelian Categories 43 Section 4: Imbedding of Abelian Categories 76 Section 5: Subquotients 88 Section 6: Left Coherent Rings 98 Section 7: Denumerable Direct Product and Denumerable Inverse Limit 112 Chapter 2. Theory of Spectral Sequences 129 Section 1: Spectral Sequences in the Ungraded Case 129 Section 2: The Spectral Sequence of an Exact Couple, Ungraded Case 143 Section 3: Graded Categories 169 Section 4: Spectral Sequences in a Graded Abelian Category 217 Section 5: The Spectral Sequence of an Exact Couple, Graded Case 240 Section 6: Filtered Objects 267 Section 7: The Partial Abutments of the Spectral Sequence of an Exact Couple 310 Section 8: The Spectral Sequence of a Filtered Cochain Complex 371 Section 9: Convergence 432 Section 10: Some Examples 473 PART I: 497 Chapter 1. The Generalized Bockstein Spectral Sequence 497 Chapter 2. The Short Exact Sequence I .8 525 Chapter 3. Cohomology of an Inverse Limit of Cochain Complexes 563 Chapter 4. Cohomology of Cochain Complexes of t-Adically Complete Left A-Modules 571 Chapter 5. Finite Generation of the Cohomology of Cochain Complexes of t-Adically Complete Left A-Modules 639 PART II: 691 Chapter 6. The Highest Non-Vanishing Cohomology Group 691 Chapter 7. Poincaré Duality 719 PART III: 769 Chapter 8. Finite Generation of the Cohomology of Cochain Complexes of I-Adically Complete Left A-Modules for a Finitely Generat 769 BIBLIOGRAPHY 833 Show more