Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.
This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's 'Big Cohen-Macaulay modules', though the complementary view point of Peskine-Szpiro and Roberts, who study the homology of certain complexes, is not neglected. Various ...
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