The Norm Residue Theorem in Motivic Cohomology

AMS-200

Christian Haesemeyer, Charles A. Weibel

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English

Princeton University Press
11 June 2019

Algebraic geometry; Topology

Series: Annals of Mathematics Studies

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 etale 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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduce the key figures behind its development.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 proceed 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.

By: Christian Haesemeyer, Charles A. Weibel
Imprint: Princeton University Press
Country of Publication: United States
Volume: 362
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691191041
ISBN 10: 0691191042
Series: Annals of Mathematics Studies
Pages: 320
Publication Date: 11 June 2019
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Christian Haesemeyer is professor in the School of Mathematics and Statistics at the University of Melbourne. Charles A. Weibel is Distinguished Professor of Mathematics at Rutgers University. He is the author of An Introduction to Homological Algebra and The K-Book: An Introduction to Algebraic K-Theory and the coauthor of Lecture Notes on Motivic Cohomology.