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" The norm residue theorem in motivic cohomology / "
Christian Haesemeyer, Charles A. Weibel.
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BL
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| Record Number
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880029
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| Main Entry
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Haesemeyer, Christian
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| Title & Author
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The norm residue theorem in motivic cohomology /\ Christian Haesemeyer, Charles A. Weibel.
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| Publication Statement
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Princeton :: Princeton University Press,, 2019.
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, ©2019
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| Series Statement
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Annals of mathematics studies ;; number 200
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xiii, 299 pages :: charts ;; 24 cm.
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| ISBN
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0691181829
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: 0691191042
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: 9780691181820
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: 9780691191041
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Includes bibliographical references (pages [283]-292) and index.
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| Contents
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Part I. An overview of the proof -- Relation to Beilinson-Lichtenbaum -- Hilbert 90 for KnM -- Rost motives and H90 -- Existence of rost motives -- Motives over S -- The motovic group H₋₁₋₁ [superscript BM] -- Part II. Degree Formulas -- Rost's chain Lemma -- Existence of norm varieties -- Existence of rost varieties -- Part III. Model structures for the A¹-homotopy category -- Cohomology operations -- Symmetric powers of motives -- Motivic classifying spaces.
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| Abstract
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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.
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| Subject
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Homology theory.
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Homology theory.
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| Dewey Classification
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514.23
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| LC Classification
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QA612.3.H34 2019
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| Added Entry
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Weibel, Charles A.,1950-
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