The logarithmic cotangent complex
نویسنده
چکیده
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.
منابع مشابه
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...
متن کاملThe 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...
متن کاملTHE 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...
متن کاملAlmost Complex Structures on the Cotangent Bundle
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Satô and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.
متن کاملDerived Algebraic Geometry IV: Deformation Theory
1 The Cotangent Complex: General Theory 4 1.1 Stable Envelopes and Tangent Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Relative Adjunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 The Tangent Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 The Relative Cotangent Complex...
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تاریخ انتشار 2005