Triangulated categories of logarithmic motives over a field

Chapter 1. Introduction
1.1. Overview
1.2. Outline of the paper
1.3. Outlook and future developments
1.4. Notations and terminology
Acknowledgements
Chapter 2. Finite logarithmic correspondences
2.1. Definition of finite log correspondences
2.2. Solid log schemes
2.3. Compositions of finite log correspondences
Chapter 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
Chapter 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/k
Chapter 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/k
Chapter 6. Calculus of fractions and homotopy theory of presheaves
6.1. Properties of localization functors
6.2. Construction of the singular functor Sing
Chapter 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 (Pn,Pn-1)-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
Chapter 8. Comparison with Voevodsky's motives
8.1. Presheaves with transfers and direct image functors
8.2. A1-local objects in logDMeff(k,)
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
Chapter 9. Hodge sheaves
9.1. Logarithmic derivations and differentials
9.2. (¶n, ¶n-1)-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
Appendix A. Logarithmic geometry
A.1. 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
Appendix B. Model structures on the category of complexes
B.1. Descent structures
Appendix C. Categorical toolbox
C.1. Category of squares
C.2. Calculus of fractions
Bibliography
Index