Triangulated categories of logarithmic motives over a field:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Société Mathématique de France
2022
|
| Series: | Astérisque
numéro 433 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 267 Seiten Diagramme |
| ISBN: | 9782856299579 |
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| 245 | 1 | 0 | |a Triangulated categories of logarithmic motives over a field |c Federico Binda, Doosung Park & Paul Arne Østvær |
| 264 | 1 | |a Paris |b Société Mathématique de France |c 2022 | |
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Record in the Search Index
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| adam_text | CONTENTS 1. Introduction ........................................................................................................ 1.1. Overview .................................................................................................. 1.2. Outline ofthepaper ................................................................................... 1.3. Outlook and futuredevelopments ........................................................... 1.4. Notations and terminology ....................................................................... Acknowledgements ............................................................................................. 1 1 7 11 13 14 2. Finite logarithmic correspondences .................................................................. 2.1. Definition of finite log correspondences .................................................. 2.2. Solid log schemes ........................................................................................ 2.3. Compositions of finite log correspondences ............................................ 17 17 19 22 3. Topologies on fine saturated logarithmic schemes .......................................... 3.1. cd-structures on fs log schemes ................................................................ 3.2. Cohomology on big and small sites ......................................................... 3.3. The dividing density structure ................................................................. 3.4. Flasque simplicial presheaves ................................................................... 27 27
30 32 43 4. Sheaves with logarithmic transfers ................................................................... 4.1. Category of presheaves with log transfers .............................................. 4.2. Compatibility with log transfers .............................................................. 4.3. Derived categories of sheaves with log transfers ................................... 4.4. Structure of dividing Nisnevich covers ................................................... 4.5. Examples of topologies compatible with log transfers ......................... 4.6. Dividing log correspondences ................................................................... 4.7. Sheaves with log transfers on SmlSm/fc ................................................. 49 49 54 61 66 69 73 76 5. Construction of triangulated categories of logarithmic motives .................... 5.1. Dividing Nisnevich cohomology groups .................................................. 5.2. Effective log motives .................................................................................. 5.3. Effective étale log motives ........................................................................ 5.4. Construction of motives using SmlSm/fc ................................................ 79 79 82 88 90 6. Calculus of fractions and homotopy theory of presheaves ............................. 6.1. Properties of localization functors ........................................................... 6.2. Construction of the singular functor Sing .............................................. 93 94 98
SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2022
CONTENTS viii 7. Properties of logarithmic motives ....................................................................... 7.1. Some toric geometry and examples of bundles ....................................... 7.2. Invariance under admissible blow-ups along smooth centers ............... 7.3. Blow-up triangles and (P ,Pn՜ ^-invariance .......................................... 7.4. Thom motives ............................................................................................... 7.5. Gysin triangles .............................................................................................. 7.6. Invariance under admissible blow-ups ...................................................... 7.7. Invariance under log modifications ........................................................... 7.8. Strictly (P։,P*-1)-invariant complexes .................................................... 103 106 110 120 124 140 145 147 150 8. Comparison with Voevodsky’s motives .............................................................. 8.1. Presheaves with transfers and direct image functors ............................ 8.2. AMocal objects in logDMeff(fe, A) .......................................................... 8.3. Projective bundle formula .......................................................................... 8.4. Motives with rational coefficients ............................................................. 8.5. Locally constant log étale sheaves ............................................................ 8.6. Comparison with Voevodsky’s étale motives
.......................................... 153 153 159 170 174 175 178 9. Hodge sheaves ...................................................................................................... 9.1. Logarithmic derivations and differentials ................................................ 9.2. (P’b Pn՜՜ ^-invariance of logarithmic differentials .................................. 9.3. A recollection on Grothendieck duality ................................................... 9.4. Cohomology with support and cycle classes ........................................... 9.5. Pushforward with proper support ............................................................ 9.6. The action of log correspondences ............................................................ 9.7. Hodge cohomology and cyclic homology ................................................. 181 181 182 187 189 194 195 201 A. Logarithmic geometry ........................................................................................ A.l. Monoids ....................................................................................................... A.2. Logarithmic structures .............................................................................. A.3. Monoschemes and fans .............................................................................. A.4. Strict morphisms ........................................................................................ A.5. Charts of logarithmic structures ............................................................. A.6. Logarithmic smoothness
........................................................................... A.7. Logarithmic differentials ........................................................................... A.8. Exact morphisms ....................................................................................... A.9. Kato-Nakayama spaces of fs log schemes ............................................... A.10. Log blow-ups ............................................................................................ A.11. Log étale monomorphisms ...................................................................... A.12. Small Kummer étale and small log étale sites .................................... A.13. Sharpened fans ........................................................................................ A.14. Frames of fs log schemes ........................................................................ 203 204 205 207 211 211 214 215 217 217 219 220 226 228 237 B. Model structures on the category of complexes ............................................... B.l. Descent structures ..................................................................................... 243 243 C. Categorical toolbox ............................................................................................ C.l. Category of squares .................................................................................. 251 251 ASTÉRISQUE 433
CONTENTS ix C.2. Calculus of fractions ................................................................................. 254 Bibliography .................................................................................................. 257 Index ............................................................................................................. 265
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| adam_txt |
CONTENTS 1. Introduction . 1.1. Overview . 1.2. Outline ofthepaper . 1.3. Outlook and futuredevelopments . 1.4. Notations and terminology . Acknowledgements . 1 1 7 11 13 14 2. Finite logarithmic correspondences . 2.1. Definition of finite log correspondences . 2.2. Solid log schemes . 2.3. Compositions of finite log correspondences . 17 17 19 22 3. Topologies on fine saturated logarithmic schemes . 3.1. cd-structures on fs log schemes . 3.2. Cohomology on big and small sites . 3.3. The dividing density structure . 3.4. Flasque simplicial presheaves . 27 27
30 32 43 4. Sheaves with logarithmic transfers . 4.1. Category of presheaves with log transfers . 4.2. Compatibility with log transfers . 4.3. Derived categories of sheaves with log transfers . 4.4. Structure of dividing Nisnevich covers . 4.5. Examples of topologies compatible with log transfers . 4.6. Dividing log correspondences . 4.7. Sheaves with log transfers on SmlSm/fc . 49 49 54 61 66 69 73 76 5. Construction of triangulated categories of logarithmic motives . 5.1. Dividing Nisnevich cohomology groups . 5.2. Effective log motives . 5.3. Effective étale log motives . 5.4. Construction of motives using SmlSm/fc . 79 79 82 88 90 6. Calculus of fractions and homotopy theory of presheaves . 6.1. Properties of localization functors . 6.2. Construction of the singular functor Sing . 93 94 98
SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2022
CONTENTS viii 7. Properties of logarithmic motives . 7.1. Some toric geometry and examples of bundles . 7.2. Invariance under admissible blow-ups along smooth centers . 7.3. Blow-up triangles and (P",Pn՜ ^-invariance . 7.4. Thom motives . 7.5. Gysin triangles . 7.6. Invariance under admissible blow-ups . 7.7. Invariance under log modifications . 7.8. Strictly (P։,P*-1)-invariant complexes . 103 106 110 120 124 140 145 147 150 8. Comparison with Voevodsky’s motives . 8.1. Presheaves with transfers and direct image functors . 8.2. AMocal objects in logDMeff(fe, A) . 8.3. Projective bundle formula . 8.4. Motives with rational coefficients . 8.5. Locally constant log étale sheaves . 8.6. Comparison with Voevodsky’s étale motives
. 153 153 159 170 174 175 178 9. Hodge sheaves . 9.1. Logarithmic derivations and differentials . 9.2. (P’b Pn՜՜ ^-invariance of logarithmic differentials . 9.3. A recollection on Grothendieck duality . 9.4. Cohomology with support and cycle classes . 9.5. Pushforward with proper support . 9.6. The action of log correspondences . 9.7. Hodge cohomology and cyclic homology . 181 181 182 187 189 194 195 201 A. Logarithmic geometry . A.l. Monoids . A.2. Logarithmic structures . A.3. Monoschemes and fans . A.4. Strict morphisms . A.5. Charts of logarithmic structures . A.6. Logarithmic smoothness
. A.7. Logarithmic differentials . A.8. Exact morphisms . A.9. Kato-Nakayama spaces of fs log schemes . A.10. Log blow-ups . A.11. Log étale monomorphisms . A.12. Small Kummer étale and small log étale sites . A.13. Sharpened fans . A.14. Frames of fs log schemes . 203 204 205 207 211 211 214 215 217 217 219 220 226 228 237 B. Model structures on the category of complexes . B.l. Descent structures . 243 243 C. Categorical toolbox . C.l. Category of squares . 251 251 ASTÉRISQUE 433
CONTENTS ix C.2. Calculus of fractions . 254 Bibliography . 257 Index . 265 |
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| spelling | Binda, Federico 1988- Verfasser (DE-588)1111915458 aut Triangulated categories of logarithmic motives over a field Federico Binda, Doosung Park & Paul Arne Østvær Paris Société Mathématique de France 2022 ix, 267 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Astérisque numéro 433 Mit einer Zusammenfassung in englischer und französischer Sprache Park, Doosung Verfasser (DE-588)1258213893 aut Østvær, Paul Arne Verfasser (DE-588)1245301721 aut Astérisque numéro 433 (DE-604)BV002579439 433 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=033636651&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Binda, Federico 1988- Park, Doosung Østvær, Paul Arne Triangulated categories of logarithmic motives over a field Astérisque |
| title | Triangulated categories of logarithmic motives over a field |
| title_auth | Triangulated categories of logarithmic motives over a field |
| title_exact_search | Triangulated categories of logarithmic motives over a field |
| title_exact_search_txtP | Triangulated categories of logarithmic motives over a field |
| title_full | Triangulated categories of logarithmic motives over a field Federico Binda, Doosung Park & Paul Arne Østvær |
| title_fullStr | Triangulated categories of logarithmic motives over a field Federico Binda, Doosung Park & Paul Arne Østvær |
| title_full_unstemmed | Triangulated categories of logarithmic motives over a field Federico Binda, Doosung Park & Paul Arne Østvær |
| title_short | Triangulated categories of logarithmic motives over a field |
| title_sort | triangulated categories of logarithmic motives over a field |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033636651&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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