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Failure of Functoriality
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Classroom Contents
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
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- 1 Intro
- 2 de Rham Cohomology for Smooth Manifolds
- 3 Example: The Variety C
- 4 Advantages of Algebraic de Rham Cohomology
- 5 The Algebraic de Rham Complex
- 6 Algebraic de Rham Cohomology in Positive Characteristic
- 7 Failure of Functoriality
- 8 Crystalline Cohomology
- 9 Drawbacks of the Crystalline Theory
- 10 Drawbacks of the de Rham-Witt Complex
- 11 Alternative Approach
- 12 Saturated Dieudonné Algebras
- 13 Proof Sketch
- 14 Conclusion
- 15 Non-Example: Completed de Rham Complexes
