Homological Questions in Local Algebra

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 refinements of Hochster''s construction obtained in collaboration with Bartijn are included. A special feature is a long chapter written by Van den Dries which explains how a certain type of result can be ''lifted'' from prime characteristic to characteristic zero. Though this is primarily a research monograph it does provide introductions to most of the topics treated. Non-experts may therefore find it an appealing guide into an active area of algebra.