Revisiting the de Rham-Witt complex:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
2021
|
| Series: | Astérisque
424 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 165 Seiten |
| ISBN: | 9782856299371 |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS 1. Introduction ........................................................................................................ 1.1. The de Rham-Witt complex ..................................................................... 1.2. Overview of the Construction .................................................................. 1.3. Motivation via the Lt? Functor ................................................................ 1.4. Notation and Terminology ........................................................................ 1.5. Prerequisites ............................................................................................... 1.6. Acknowledgments ....................................................................................... Parti. Construction of 1 1 2 6 8 9 9 ................................................................................ 11 2. Dieudonné Complexes ....................................................................................... 2.1. The Category 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 Μ* with ............................................................. 2.9. More on Strict Dieudonné Towers ........................................................... 13 13 14 15 16 19 21 23 26 27 3. Dieudonné Algebras ........................................................................................... 3.1. The Category 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 ..................................................................... 29 29 31 33 35 36 38 41 4. The Saturated de Rham-Witt Complex ............................................................ 4.1. Construction of Ωβ ............................................................................... 4.2. Comparison with a Smooth Lift .............................................................. 4.3. Comparison with the de Rham Complex ............................................... 4.4.
The Classical de Rham-Witt Complex ................................................... 43 43 45 46 48 5. Localizations of Dieudonné Algebras ............................................................... 5.1. Localization for the Zariski Topology ..................................................... 55 55 It SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2021
CONTENTS viii The saturated de Rham-Witt Complex of an Fp-Scheme .................... Localization for the étale Topology ......................................................... Digression: Witt Vectors and étale Morphisms ..................................... The Proof of Theorem 5.3.4 ..................................................................... 58 60 63 θθ 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 ...................................................................... 71 72 73 74 75 76 78 Partii. Complements and Applications .............................................................. 81 7. Homological Algebra.......................................................................................... 7.1. p-Complete Objects of the Derived Category ........................................ 7.2. The Functor Εηρ ........................................................................................ 7.3. Fixed Points of Lηp■. 1-Categorical Version ............................................ 7.4. Fixed Points of Lz/P:
oo-Categorical Version ......................................... 7.5. The Proof of Theorem 7.4.7 ..................................................................... 7.6. Tensor Products of Strict Dieudonné Complexes .................................. 83 84 87 89 92 95 98 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 Σ,ηρ via Filtered Derived Categories . .. 103 104 105 107 108 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 ................... 113 113 115 117 122 125 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 ...................................................... 133 133 135 141 145 11. The Crystalline Comparison for ΑΩ ............................................................... 11.1. Review of the Construction of ΑΩ ........................................................ 11.2. The First Formulation of the Main Comparison Theorem ................ 11.3. Extracting a Presheaf of Strict Dieudonné Algebras from ΑΩχ .... 11.4. Comparison with the de Rham-Witt Complex .................................... 147 147 149 150 156 Bibliography ............................................................................................................ 161 5.2. 5.3. 5.4. 5.5. ASTÉRISQUE 424
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| adam_txt |
CONTENTS 1. Introduction . 1.1. The de Rham-Witt complex . 1.2. Overview of the Construction . 1.3. Motivation via the Lt? Functor . 1.4. Notation and Terminology . 1.5. Prerequisites . 1.6. Acknowledgments . Parti. Construction of 1 1 2 6 8 9 9 . 11 2. Dieudonné Complexes . 2.1. The Category 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 Μ* with . 2.9. More on Strict Dieudonné Towers . 13 13 14 15 16 19 21 23 26 27 3. Dieudonné Algebras . 3.1. The Category 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 . 29 29 31 33 35 36 38 41 4. The Saturated de Rham-Witt Complex . 4.1. Construction of Ωβ . 4.2. Comparison with a Smooth Lift . 4.3. Comparison with the de Rham Complex . 4.4.
The Classical de Rham-Witt Complex . 43 43 45 46 48 5. Localizations of Dieudonné Algebras . 5.1. Localization for the Zariski Topology . 55 55 It SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2021
CONTENTS viii The saturated de Rham-Witt Complex of an Fp-Scheme . Localization for the étale Topology . Digression: Witt Vectors and étale Morphisms . The Proof of Theorem 5.3.4 . 58 60 63 θθ 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 . 71 72 73 74 75 76 78 Partii. Complements and Applications . 81 7. Homological Algebra. 7.1. p-Complete Objects of the Derived Category . 7.2. The Functor Εηρ . 7.3. Fixed Points of Lηp■. 1-Categorical Version . 7.4. Fixed Points of Lz/P:
oo-Categorical Version . 7.5. The Proof of Theorem 7.4.7 . 7.6. Tensor Products of Strict Dieudonné Complexes . 83 84 87 89 92 95 98 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 Σ,ηρ via Filtered Derived Categories . . 103 104 105 107 108 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 . 113 113 115 117 122 125 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 . 133 133 135 141 145 11. The Crystalline Comparison for ΑΩ . 11.1. Review of the Construction of ΑΩ . 11.2. The First Formulation of the Main Comparison Theorem . 11.3. Extracting a Presheaf of Strict Dieudonné Algebras from ΑΩχ . 11.4. Comparison with the de Rham-Witt Complex . 147 147 149 150 156 Bibliography . 161 5.2. 5.3. 5.4. 5.5. ASTÉRISQUE 424 |
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| isbn | 9782856299371 |
| language | English |
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| spelling | Bhatt, Bhargav Verfasser (DE-588)1193438020 aut Revisiting the de Rham-Witt complex Bhargav Bhatt, Jacob Lurie & Akhil Mathew Paris Société Mathématique de France 2021 © 2020 viii, 165 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 424 Mit einer Zusammenfassung in englischer und französischer Sprache Lurie, Jacob 1977- Verfasser (DE-588)139905529 aut Mathew, Akhil Verfasser (DE-588)1236164709 aut Astérisque 424 (DE-604)BV002579439 424 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032763200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhatt, Bhargav Lurie, Jacob 1977- Mathew, Akhil Revisiting the de Rham-Witt complex Astérisque |
| title | Revisiting the de Rham-Witt complex |
| title_auth | Revisiting the de Rham-Witt complex |
| title_exact_search | Revisiting the de Rham-Witt complex |
| title_exact_search_txtP | Revisiting the de Rham-Witt complex |
| title_full | Revisiting the de Rham-Witt complex Bhargav Bhatt, Jacob Lurie & Akhil Mathew |
| title_fullStr | Revisiting the de Rham-Witt complex Bhargav Bhatt, Jacob Lurie & Akhil Mathew |
| title_full_unstemmed | Revisiting the de Rham-Witt complex Bhargav Bhatt, Jacob Lurie & Akhil Mathew |
| title_short | Revisiting the de Rham-Witt complex |
| title_sort | revisiting the de rham witt complex |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032763200&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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