Homological invariants of modules over commutative rings (Seminaire de mathematiques superieures)

Homological Invariants of Modules over Commutative Rings......Page 1 Table of Contents......Page 5 Introduction......Page 6 1. Finite free resolutions and Betti numbers of modules......Page 8 2. Minimal injective resolutions of modules......Page 15 3. Injective modules over commutative Noetherian rings and Bass numbers of modules......Page 20 4. Properties of Bass numbers of modules; relations to depth and dimension......Page 24 2. Applications of local duality......Page 33 1. Elementary Matlis duality......Page 34 2. Generalization to complexes......Page 36 3. Local duality......Page 47 4. Applications......Page 58 1. The new intersection conjecture......Page 64 2. Local cohomology......Page 70 3. Killing local cohomology through desingularization......Page 78 4. Minimal free resolutions of determinantal ideals......Page 85 References......Page 102