Spectrum of a Module Category.

Intro -- Contents -- Chapter 0. Introduction -- Chapter 1. The functor category -- 1.1. Preliminaries -- 1.2. Purity -- Chapter 2. Definable subcategories -- 2.1. Definable subcategories -- 2.2. Saturation -- 2.3. The Ziegler topology -- 2.4. Definable quotient categories -- 2.5. Examples -- Chapter 3. Left approximations -- 3.1. Left almost split maps -- 3.2. Left approximations -- 3.3. Minimal left approximations -- Chapter 4. Duality -- 4.1. Purely equivalent and purely opposed modules -- 4.2. The dual of a definable subcategory -- 4.3. Pure-reflexive modules -- Chapter 5. Ideals in the category of finitely presented modules -- 5.1. Fp-idempotent ideals -- 5.2. Ideals generated by idempotents -- Chapter 6. Endofinite modules -- 6.1. The endocategory of a module -- 6.2. ∑-pure-injective modules -- 6.3. Product-complete modules -- 6.4. Endofinite modules -- 6.5. Generic modules -- 6.6. Ideals of finite length -- Chapter 7. Krull-Gabriel dimension -- 7.1. The Krull-Gabriel dimension of a ring -- 7.2. The Krull-Gabriel dimension of a module -- Chapter 8. The infinite radical -- 8.1. The preinjective dimension of a module -- 8.2. Transfinite powers of the Jacobson radical -- Chapter 9. Functors between module categories -- 9.1. Coherent functors -- Chapter 10. Tame algebras -- 10.1. Endofinitely tame algebras -- 10.2. Functors preserving tameness -- 10.3. Representation embeddings -- 10.4. One-parameter families and generic modules -- Chapter 11. Rings of definable scalars -- 11.1. Rings of definable scalars -- 11.2. Calculus of fractions -- 11.3. Biendomorphism rings -- 11.4. Basic properties -- 11.5. Epimorphisms of rings -- Chapter 12. Reflective definable subcategories -- 12.1. Reflective definable subcategories -- 12.2. Φ-continuous modules -- 12.3. Definable and universal localizations -- Chapter 13. Sheaves.

13.1. Sheaves on the Gabriel spectrum -- 13.2. The Zariski topology -- 13.3. Structure sheaves -- 13.4. Associated sheaves of modules -- Chapter 14. Tame hereditary algebras -- 14.1. Preliminaries -- 14.2. A parametrizing curve -- Chapter 15. Coherent rings -- 15.1. Preliminaries -- 15.2. Prime spectrum versus Gabriel spectrum -- 15.3. The global section functor -- Appendix A. Locally coherent Grothendieck categories -- A.1. Localization in abelian categories -- A.2. Locally coherent Grothendieck categories -- A.3. Localization in locally coherent Grothendieck categories -- A.4. Locally noetherian categories -- Appendix B. Dimensions -- B.1. The dimension of an abelian category -- B.2. The dimension of a modular lattice -- Appendix C. Finitely presented functors and ideals -- C.1. The category of finitely presented functors -- C.2. Ideals in additive categories -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.