Revisiting the de Rham-Witt complex

Chapter 1. Introduction
1.1. The de Rham-Witt complex
1.2. Overview of the Construction
1.3. Motivation via the L Functor
1.4. Notation and Terminology
1.5. Prerequisites
1.6. Acknowledgments
Part I. Construction of WR
Chapter 2. Dieudonné Complexes
2.1. The Category `39`42`"613A``45`47`"603A DC
2.2. Saturated Dieudonné Complexes
2.3. Saturation of Dieudonné Complexes
2.4. The Cartier Criterion
2.5. Strict Dieudonné Complexes
2.6. Strict Dieudonné Towers
2.7. The Completion of a Saturated Dieudonné Complex
2.8. Comparison of M with `39`42`"613A``45`47`"603A W (M)
2.9. More on Strict Dieudonné Towers
Chapter 3. Dieudonné Algebras
3.1. The Category `39`42`"613A``45`47`"603A DA
3.2. Example: The de Rham Complex
3.3. The Cartier Isomorphism
3.4. Saturated Dieudonné Algebras
3.5. Completions of Saturated Dieudonné Algebras
3.6. Comparison with Witt Vectors
3.7. Aside: Rings with p-Torsion
Chapter 4. The Saturated de Rham-Witt Complex
4.1. Construction of `39`42`"613A``45`47`"603A `39`42`"613A``45`47`"603A W R
4.2. Comparison with a Smooth Lift
4.3. Comparison with the de Rham Complex
4.4. The Classical de Rham-Witt Complex
Chapter 5. Localizations of Dieudonné Algebras
5.1. Localization for the Zariski Topology
5.2. The saturated de Rham-Witt Complex of an Fp-Scheme
5.3. Localization for the étale Topology
5.4. Digression: Witt Vectors and étale Morphisms
5.5. The proof of Theorem 5.3.4
Chapter 6. The Case of a Cusp
6.1. Digression: The de Rham Complex of a Graded Ring
6.2. The Saturated de Rham-Witt Complex of a Cusp
6.3. The Classical de Rham-Witt Complex of a Cusp
6.4. The Crystalline Cohomology of a Cusp
6.5. Seminormality
6.6. The Proof of Theorem 6.5.3
Part II. Complements and Applications
Chapter 7. Homological Algebra
7.1. p-Complete Objects of the Derived Category
7.2. The Functor Lp
7.3. Fixed Points of L p: 1-Categorical Version
7.4. Fixed Points of L p: -Categorical Version
7.5. The Proof of Theorem 7.4.7
7.6. Tensor Products of Strict Dieudonné Complexes
Chapter 8. The Nygaard Filtration
8.1. The Nygaard Filtration of a Saturated Dieudonné Complex
8.2. The Nygaard Filtration of a Completion
8.3. Dieudonné Complexes of Cartier Type
8.4. The Nygaard Filtration and Lp via Filtered Derived Categories
Chapter 9. The Derived de Rham-Witt Complex
9.1. Lax Fixed Points
9.2. Digression: Nonabelian Derived Functors
9.3. Saturated Derived Crystalline Cohomology
9.4. Comparison with the de Rham complex
9.5. The de Rham comparison for regular Fp-algebras, redux
Chapter 10. Comparison with Crystalline Cohomology
10.1. Introduction
10.2. Construction of the Comparison Map
10.3. Endomorphisms of the de Rham Functor
10.4. Uniqueness of the Comparison Map
Chapter 11. The Crystalline Comparison for A
11.1. Review of the Construction of A
11.2. The First Formulation of the Main Comparison Theorem
11.3. Extracting a Presheaf of Strict Dieudonné Algebras from AX
11.4. Comparison with the de Rham-Witt Complex
Bibliography