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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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2019] ©2019 |
| Year of Publication: | 2019 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
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| Physical Description: | 1 online resource (320 p.) |
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Haesemeyer, Christian, author. aut http://id.loc.gov/vocabulary/relators/aut The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / Charles A. Weibel, Christian Haesemeyer. Princeton, NJ : Princeton University Press, [2019] ©2019 1 online resource (320 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 375 Frontmatter -- Contents -- Preface -- Acknowledgments -- Part I -- 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 -- Part II -- 8. Degree Formulas -- 9. Rost's Chain Lemma -- 10. Existence of Norm Varieties -- 11. Existence of Rost Varieties -- Part III -- 12. Model Structures for the A1-homotopy Category -- 13. Cohomology Operations -- 14. Symmetric Powers of Motives -- 15. Motivic Classifying Spaces -- Glossary -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduce the key figures behind its development.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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Homology theory. MATHEMATICS / Geometry / Algebraic. bisacsh 5P. Abelian group. Addition. Additive category. Adjoint functors. Alexander Grothendieck. Algebraic closure. Algebraic cobordism. Algebraic cycle. Algebraic extension. Algebraic geometry. Algebraic topology. Andrei Suslin. Axiom. Characteristic class. Classifying space. Closed set. Codimension. Cofibration. Cohomology operation. Cohomology. Conjecture. Corollary. Diagram (category theory). Direct limit. Exact sequence. Factorization. Fibration. Functor. Galois cohomology. Galois extension. Group object. Homology (mathematics). Homotopy category. Homotopy. Hypersurface. Inverse function. Mathematical induction. Mathematics. Milnor K-theory. Model category. Module (mathematics). Monoid. Monomorphism. Morphism. Motivic cohomology. Natural number. Normal bundle. Open set. Presheaf (category theory). Pushout (category theory). Quantity. Quillen adjunction. Rational point. Regular representation. Remainder. Retract. Separable extension. Sheaf (mathematics). Smooth scheme. Special case. Subgroup. Summation. Tangent space. Theorem. Trivial representation. Vladimir Voevodsky. Weak equivalence (homotopy theory). Weibel, Charles A., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English 9783110610765 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 9783110664232 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English 9783110610406 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 9783110606362 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2019 9783110663365 print 9780691181820 https://doi.org/10.1515/9780691189635?locatt=mode:legacy https://www.degruyter.com/isbn/9780691189635 Cover https://www.degruyter.com/document/cover/isbn/9780691189635/original |
| language |
English |
| format |
eBook |
| author |
Haesemeyer, Christian, Haesemeyer, Christian, Weibel, Charles A., |
| spellingShingle |
Haesemeyer, Christian, Haesemeyer, Christian, Weibel, Charles A., The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- Acknowledgments -- Part I -- 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 -- Part II -- 8. Degree Formulas -- 9. Rost's Chain Lemma -- 10. Existence of Norm Varieties -- 11. Existence of Rost Varieties -- Part III -- 12. Model Structures for the A1-homotopy Category -- 13. Cohomology Operations -- 14. Symmetric Powers of Motives -- 15. Motivic Classifying Spaces -- Glossary -- Bibliography -- Index |
| author_facet |
Haesemeyer, Christian, Haesemeyer, Christian, Weibel, Charles A., Weibel, Charles A., Weibel, Charles A., |
| author_variant |
c h ch c h ch c a w ca caw |
| author_role |
VerfasserIn VerfasserIn VerfasserIn |
| author2 |
Weibel, Charles A., Weibel, Charles A., |
| author2_variant |
c a w ca caw |
| author2_role |
VerfasserIn VerfasserIn |
| author_sort |
Haesemeyer, Christian, |
| title |
The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / |
| title_sub |
(AMS-200) / |
| title_full |
The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / Charles A. Weibel, Christian Haesemeyer. |
| title_fullStr |
The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / Charles A. Weibel, Christian Haesemeyer. |
| title_full_unstemmed |
The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / Charles A. Weibel, Christian Haesemeyer. |
| title_auth |
The Norm Residue Theorem in Motivic Cohomology : (AMS-200) / |
| title_alt |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Part I -- 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 -- Part II -- 8. Degree Formulas -- 9. Rost's Chain Lemma -- 10. Existence of Norm Varieties -- 11. Existence of Rost Varieties -- Part III -- 12. Model Structures for the A1-homotopy Category -- 13. Cohomology Operations -- 14. Symmetric Powers of Motives -- 15. Motivic Classifying Spaces -- Glossary -- Bibliography -- Index |
| title_new |
The Norm Residue Theorem in Motivic Cohomology : |
| title_sort |
the norm residue theorem in motivic cohomology : (ams-200) / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2019 |
| physical |
1 online resource (320 p.) Issued also in print. |
| contents |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Part I -- 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 -- Part II -- 8. Degree Formulas -- 9. Rost's Chain Lemma -- 10. Existence of Norm Varieties -- 11. Existence of Rost Varieties -- Part III -- 12. Model Structures for the A1-homotopy Category -- 13. Cohomology Operations -- 14. Symmetric Powers of Motives -- 15. Motivic Classifying Spaces -- Glossary -- Bibliography -- Index |
| isbn |
9780691189635 9783110610765 9783110664232 9783110610406 9783110606362 9783110494914 9783110663365 9780691181820 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA612 |
| callnumber-sort |
QA 3612.3 |
| url |
https://doi.org/10.1515/9780691189635?locatt=mode:legacy https://www.degruyter.com/isbn/9780691189635 https://www.degruyter.com/document/cover/isbn/9780691189635/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
514 - Topology |
| dewey-full |
514.23 |
| dewey-sort |
3514.23 |
| dewey-raw |
514.23 |
| dewey-search |
514.23 |
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10.1515/9780691189635?locatt=mode:legacy |
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1090539960 |
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