The Cotangent Complex of a Morphism

The logarithmic cotangent complex

We define the cotangent complex of a morphism of fine log schemes, prove that it is functorial, and construct under certain restrictions a transitivity triangle. We also discuss its relationship with deformation theory.

THE COTANGENT COMPLEX Contents

Contents 1. Introduction 1 2. Advice for the reader 2 3. The cotangent complex of a ring map 2 4. Simplicial resolutions and derived lower shriek 3 5. Constructing a resolution 6 6. Functoriality 11 7. The fundamental triangle 13 8. Localization andétale ring maps 17 9. Smooth ring maps 19 10. Comparison with the naive cotangent complex 19 11. A spectral sequence of Quillen 21 12. Comparison wi...

The Cotangent Complex

08P5 Contents 1. Introduction 1 2. Advice for the reader 2 3. The cotangent complex of a ring map 2 4. Simplicial resolutions and derived lower shriek 3 5. Constructing a resolution 6 6. Functoriality 11 7. The fundamental triangle 13 8. Localization andétale ring maps 17 9. Smooth ring maps 19 10. Comparison with the naive cotangent complex 19 11. A spectral sequence of Quillen 21 12. Comparis...

THE COTANGENT COMPLEX Contents

Contents 1. Introduction 1 2. Advice for the reader 2 3. The cotangent complex of a ring map 2 4. Simplicial resolutions and derived lower shriek 3 5. Constructing a resolution 6 6. Functoriality 11 7. The fundamental triangle 13 8. Localization andétale ring maps 17 9. Smooth ring maps 19 10. Comparison with the naive cotangent complex 19 11. A spectral sequence of Quillen 21 12. Comparison wi...

The Cotangent Complex 08p5