The Norm Residue Theorem in Motivic Cohomology : : (AMS-200) /

The Norm Residue Theorem in Motivic Cohomology : : (AMS-200) / / Charles A. Weibel, Christian Haesemeyer.

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 Cho...

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Superior document:Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English
VerfasserIn:
Haesemeyer, Christian,
Weibel, Charles A.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2019]
©2019
Year of Publication:2019
Language:English
Series:Annals of Mathematics Studies ; 375
Online Access:
Physical Description:1 online resource (320 p.)
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100 1 |a Haesemeyer, Christian,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Norm Residue Theorem in Motivic Cohomology :  |b (AMS-200) /  |c Charles A. Weibel, Christian Haesemeyer. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2019] 
264 4 |c ©2019 
300 |a 1 online resource (320 p.) 
336 |a text  |b txt  |2 rdacontent 
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490 0 |a Annals of Mathematics Studies ;  |v 375 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Acknowledgments --   |t Part I --   |t 1. An Overview of the Proof --   |t 2. Relation to Beilinson-Lichtenbaum --   |t 3. Hilbert 90 for KMn --   |t 4. Rost Motives and H90 --   |t 5. Existence of Rost Motives --   |t 6. Motives over S --   |t 7. The Motivic Group HBM−1,−1 --   |t Part II --   |t 8. Degree Formulas --   |t 9. Rost's Chain Lemma --   |t 10. Existence of Norm Varieties --   |t 11. Existence of Rost Varieties --   |t Part III --   |t 12. Model Structures for the A1-homotopy Category --   |t 13. Cohomology Operations --   |t 14. Symmetric Powers of Motives --   |t 15. Motivic Classifying Spaces --   |t Glossary --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Homology theory. 
650 7 |a MATHEMATICS / Geometry / Algebraic.  |2 bisacsh 
653 |a 5P. 
653 |a Abelian group. 
653 |a Addition. 
653 |a Additive category. 
653 |a Adjoint functors. 
653 |a Alexander Grothendieck. 
653 |a Algebraic closure. 
653 |a Algebraic cobordism. 
653 |a Algebraic cycle. 
653 |a Algebraic extension. 
653 |a Algebraic geometry. 
653 |a Algebraic topology. 
653 |a Andrei Suslin. 
653 |a Axiom. 
653 |a Characteristic class. 
653 |a Classifying space. 
653 |a Closed set. 
653 |a Codimension. 
653 |a Cofibration. 
653 |a Cohomology operation. 
653 |a Cohomology. 
653 |a Conjecture. 
653 |a Corollary. 
653 |a Diagram (category theory). 
653 |a Direct limit. 
653 |a Exact sequence. 
653 |a Factorization. 
653 |a Fibration. 
653 |a Functor. 
653 |a Galois cohomology. 
653 |a Galois extension. 
653 |a Group object. 
653 |a Homology (mathematics). 
653 |a Homotopy category. 
653 |a Homotopy. 
653 |a Hypersurface. 
653 |a Inverse function. 
653 |a Mathematical induction. 
653 |a Mathematics. 
653 |a Milnor K-theory. 
653 |a Model category. 
653 |a Module (mathematics). 
653 |a Monoid. 
653 |a Monomorphism. 
653 |a Morphism. 
653 |a Motivic cohomology. 
653 |a Natural number. 
653 |a Normal bundle. 
653 |a Open set. 
653 |a Presheaf (category theory). 
653 |a Pushout (category theory). 
653 |a Quantity. 
653 |a Quillen adjunction. 
653 |a Rational point. 
653 |a Regular representation. 
653 |a Remainder. 
653 |a Retract. 
653 |a Separable extension. 
653 |a Sheaf (mathematics). 
653 |a Smooth scheme. 
653 |a Special case. 
653 |a Subgroup. 
653 |a Summation. 
653 |a Tangent space. 
653 |a Theorem. 
653 |a Trivial representation. 
653 |a Vladimir Voevodsky. 
653 |a Weak equivalence (homotopy theory). 
700 1 |a Weibel, Charles A.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press Complete eBook-Package 2019  |z 9783110663365 
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912 |a 978-3-11-061076-5 EBOOK PACKAGE COMPLETE 2019 English  |b 2019 
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