TY  - BOOK
AU  - Ferretti,Andrea
TI  - Homological methods in commutative algebra
T2  - Graduate studies in mathematics
SN  - 9781470474362
U1  - 512.55  23
PY  - 2024///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Commutative algebra
KW  - Algebra, Homological
KW  - Modules (Algebra)
KW  - Category theory
KW  - Algebraic geometry
N1  - Includes bibliographical references and index; Categories and functors -- Abelian categories -- Derived functors -- Spectral sequences -- Projective and injective modules -- Flatness -- Koszul complexes and regular sequences -- Regularity -- Mild singularities -- Local cohomology and duality
N2  - This advanced textbook develops the machinery of homological algebra and demonstrates its applications in commutative algebra. Beginning with category theory and Abelian categories, the book systematically introduces derived functors, Ext and Tor modules, spectral sequences, projective and injective modules, flatness, regular sequences, local cohomology, and duality theory. The author carefully connects abstract homological methods with the structural study of commutative rings and modules, including regular rings, Cohen-Macaulay rings, Gorenstein rings, and complete intersections. Numerous examples, exercises, and theoretical discussions illustrate the interaction between algebra, topology, algebraic geometry, and homological techniques. Written for graduate students and researchers, the work provides a rigorous yet accessible introduction to modern homological methods in commutative algebra and related mathematical disciplines
ER  -