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Interactions between Homotopy Theory and Algebra
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Otros Autores: | , |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2007.
|
| Colección: | Contemporary Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Contents""; ""Preface""; ""List of Participants""; ""Introductory Lecture Series""; ""Model Categories and Simplicial Methods""; ""1. Model Categories and Resolutions""; ""2. Quillen Functors and Derived Functors""; ""3. Generating New Model Categories""; ""4. Simplicial Algebras and Resolutions in Non-abelian Settings""; ""5. Resolutions in Model Categories""; ""References""; ""Lectures on Local Cohomology""; ""1. Introduction""; ""2. Local Cohomology""; ""3. Injective Modules over Noetherian Rings and Matlis Duality""; ""4. Cohen-Macaulay and Gorenstein rings""
- ""5. Vanishing Theorems and the Structure of Hdm(R)""""6. Vanishing Theorems II""; ""7. Appendix 1: Using local cohomology to prove a result of Kalkbrenner and Sturmfels""; ""8. Appendix 2: Bass numbers and Gorenstein Rings""; ""References""; ""Derived categories, resolutions, and Brown representability""; ""Introduction""; ""1. Derived categories""; ""1.1. Additive and abelian categories""; ""1.2. Categories of complexes""; ""1.3. Localization""; ""1.4. An alternative definition""; ""1.5. Extension groups""; ""1.6. Hereditary categories""; ""1. 7. Bounded derived categories""; ""1.8. Notes""
- ""2. Triangulated categories""""2.1. The axioms""; ""2.2. The octahedral axiom""; ""2.3. Cohomological functors""; ""2.4. Uniqueness of exact triangles""; ""2.5. K(A) is triangulated""; ""2.6. Notes""; ""3. Localization of triangulated categories""; ""3.1. Quasi-isomorphisms""; ""3.2. D(A) is triangulated""; ""3.3. Triangulated and thick subcategories""; ""3.4. The kernel of a localization""; ""3.5. Verdier localization""; ""3.6. Notes""; ""4. Brown representability""; ""4.1. Coherent functors""; ""4.2. The abelianization of a triangulated category""
- ""4.3. The idempotent completion of a triangulated category""""4.4. Homotopy colimits""; ""4.5. Brown representability""; ""4.6. Notes""; ""5. Resolutions""; ""5.1. Injective resolutions""; ""5.2. Projective Resolutions""; ""5.3. Derived functors""; ""5.4. Notes""; ""6. Differential graded algebras and categories""; ""6.1. Differential graded algebras and modules""; ""6.2. Differential graded categories""; ""6.3. Duality""; ""6.4. Injective and projective resolutions""; ""6.5. Compact objects and perfect complexes""; ""6.6. Notes""; ""7. Algebraic triangulated categories""
- ""7.1. Exact categories""""7.2. Frobenius categories""; ""7.3. The derived category of an exact category""; ""7.4. The stable category of a Frobenius category""; ""7.5. Algebraic triangulated categories""; ""7.6. The stable homotopy category is not algebraic""; ""7. 7. The differential graded category of an exact category""; ""7.8. Notes""; ""Appendix A. The octahedral axiom""; ""References""; ""Exercises on derived categories, resolutions, and Brown representability""; ""Topics Lecture Series""; ""Spectra for commutative algebraists""; ""0. Introduction.""