The Norm Residue Theorem in Motivic Cohomology

Name: The Norm Residue Theorem in Motivic Cohomology | (AMS-200)
Brand: Princeton University Press
Price: 391.95 EUR
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(AMS-200)

Christian Haesemeyer Charles A. Weibel(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 11. Juni 2019

320 Seiten

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Inhalt

Cover
Contents
Preface
Acknowledgments
Part I
1. An Overview of the Proof
1.1 First Reductions
1.2 The Quick Proof
1.3 Norm Varieties and Rost Varieties
1.4 The Beilinson-Lichtenbaum Conditions
1.5 Simplicial Schemes
1.6 Motivic Cohomology Operations
1.7 Historical Notes
2. Relation to Beilinson-Lichtenbaum
2.1 BL(n) Implies BL(n-1)
2.2 H90(n) Implies H90(n-1)
2.3 Cohomology of Singular Varieties
2.4 Cohomology with Supports
2.5 Rationally Contractible Presheaves
2.6 Bloch-Kato Implies Beilinson-Lichtenbaum
2.7 Condition H90(n) Implies BL(n)
2.8 Historical Notes
3. Hilbert 90 for KMn
3.1 Hilbert 90 for KMn
3.2 A Galois Cohomology Sequence
3.3 Hilbert 90 for l-special Fields
3.4 Cohomology Elements
3.5 Historical Notes
4. Rost Motives and H90
4.1 Chow Motives
4.2 X-Duality
4.3 Rost Motives
4.4 Rost Motives Imply Hilbert 90
4.5 Historical Notes
5. Existence of Rost Motives
5.1 A Candidate for the Rost Motive
5.2 Axioms (ii) and (iii)
5.3 End(M) Is a Local Ring
5.4 Existence of a Rost Motive
5.5 Historical Notes
6. Motives over S
6.1 Motives over a Scheme
6.2 Motives over a Simplicial Scheme
6.3 Motives over a Smooth Simplicial Scheme
6.4 The Slice Filtration
6.5 Embedded Schemes
6.6 The Operations Øi
6.7 The Operation ØV
6.8 Historical Notes
7. The Motivic Group HBM-1,-1
7.1 Properties of H-1,-1
7.2 The Case of Norm Varieties
7.3 Historical Notes
Part II
8. Degree Formulas
8.1 Algebraic Cobordism
8.2 The General Degree Formula
8.3 Other Degree Formulas
8.4 An Equivariant Degree Formula
8.5 The n-invariant
8.6 Historical Notes
9. Rost's Chain Lemma
9.1 Forms on Vector Bundles
9.2 The Chain Lemma when n=2
9.3 The Symbol Chain
9.4 The Tower of Varieties Pr and Qr
9.5 Models for Moves of Type Cn
9.6 Proof of the Chain Lemma
9.7 Nice G-actions
9.8 Chain Lemma, Revisited
9.9 Historical Notes
10. Existence of Norm Varieties
10.1 Properties of Norm Varieties
10.2 Two vn-1-varieties
10.3 Norm Varieties Are vn-1-varieties
10.4 Existence of Norm Varieties
10.5 Historical Notes
11. Existence of Rost Varieties
11.1 The Multiplication Principle
11.2 The Norm Principle
11.3 Weil Restriction
11.4 Another Splitting Variety
11.5 Expressing Norms
11.6 Historical Notes
Part III
12. Model Structures for the A1-homotopy Category
12.1 The Projective Model Structure
12.2 Radditive Presheaves
12.3 The Radditive Projective Model Structure
12.4 ?-closed Classes and Weak Equivalences
12.5 Bousfield Localization
12.6 Bousfield Localization and ?-closed Classes
12.7 Nisnevich-Local Projective Model Structure
12.8 Model Categories of Sheaves
12.9 A1-local Model Structure
12.10 Historical Notes
13. Cohomology Operations
13.1 Motivic Cohomology Operations
13.2 Steenrod Operations
13.3 Construction of Steenrod Operations
13.4 The Milnor Operations Qi
13.5 Qn of the Degree Map
13.6 Margolis Homology
13.7 A Motivic Degree Theorem
13.8 Historical Notes
14. Symmetric Powers of Motives
14.1 Symmetric Powers of Varieties
14.2 Symmetric Powers of Correspondences
14.3 Weak Equivalences and Symmetric Powers
14.4 SG of Quotients X/U
14.5 Nisnevich G-local Equivalences
14.6 Symmetric Powers and Shifts
14.7 Historical Notes
15. Motivic Classifying Spaces
15.1 Symmetric Powers and Operations
15.2 Operations on H1,1
15.3 Scalar Weight
15.4 The Motive of (V -0)/C with VC =0
15.5 The Motive Sltr(Ln)
15.6 A Künneth Formula
15.7 Operations of Pure Scalar Weight
15.8 Uniqueness of ßPn
15.9 Historical Notes
Glossary
Bibliography
Index

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