A commutative P¹-spectrum representing motivic cohomology over dedekind domains

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Author(s): Markus Spitzweck
Series: Mémoires de la Société Mathématique de France. Nouvelle série
Publisher: SMF
Year: 2018

Language: English

Chapter 1. Introduction
Acknowledgements
Chapter 2. Preliminaries and Notation
Chapter 3. Motivic complexes I
Chapter 4. The construction
4.1. The p-parts
4.1.1. Finite coefficients
4.1.2. The p-completed parts
4.2. The completed part
4.3. The rational parts
4.4. The definition
Chapter 5. Motivic Complexes II
5.1. A strictification
5.2. Properties of the motivic complexes
5.2.1. Comparison to flat maps
5.2.2. Some localization triangles
5.2.3. The étale cycle class map
5.3. The naive Gm-spectrum
Chapter 6. Motivic complexes over a field
Chapter 7. Comparisons
7.1. The exceptional inverse image of M
7.2. Pullback to the generic point
7.3. Weight 1 motivic complexes
7.4. Rational spectra
7.5. The isomorphism between MZ and M
Chapter 8. Base change
Chapter 9. The motivic functor formalism
Chapter 10. Further applications
10.1. The Hopkins-Morel isomorphism
10.2. The dual motivic Steenrod algebra
Appendix A. (Semi) model structures
Appendix B. Pullback of cycles
Appendix C. An explicit periodization of MZ
Bibliography