Contents
Preface
Introduction
Lecture 1. Basic Notions
§1. Algebraic sets
§2. Krull dimension of a ring
§3. Dimension of an algebraic set
§4. An extended example
§5. Tangent spaces and regular rings
§6. Dimension of a module
Lecture 2. Cohomology
§1. Sheaves
§2. Cech cohomology
§3. Calculus versus topology
§4. Cech cohomology and derived functors
Lecture 3. Resolutions and Derived Functors
§1. Free, projective, and flat modules
§2. Complexes
§3. Resolutions
§4. Derived functors
Lecture 4. Limits
§1. An example from topology
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