The Norm Residue Theorem in Motivic Cohomology / Charles A. Weibel, Christian Haesemeyer.

Format:

Book

Author/Creator:

Haesemeyer, Christian, Author.

Weibel, Charles A., Author.

Series:

Annals of mathematics studies ; 200.

Princeton scholarship online.

Annals of Mathematics Studies ; 200

Language:

English

Subjects (All):

Homology theory.

Physical Description:

1 online resource (317 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2019]

Language Note:

In English.

Summary:

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups.Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduce the key figures behind its development. They go on to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations.Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

Contents:

Frontmatter

Contents

Preface

Acknowledgments

1. An Overview of the Proof

2. Relation to Beilinson-Lichtenbaum

3. Hilbert 90 for KMn

4. Rost Motives and H90

5. Existence of Rost Motives

6. Motives over S

7. The Motivic Group HBM−1,−1

8. Degree Formulas

9. Rost's Chain Lemma

10. Existence of Norm Varieties

11. Existence of Rost Varieties

12. Model Structures for the A1-homotopy Category

13. Cohomology Operations

14. Symmetric Powers of Motives

15. Motivic Classifying Spaces

Glossary

Bibliography

Index

Notes:

Previously issued in print: 2019.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020)

ISBN:

9780691189635

0691189633

OCLC:

1090539960