Norm Residue Theorem in Motivic Cohomology (eBook)

(AMS-200)

Christian Haesemeyer, Charles A. Weibel (Autoren)

eBook Download: PDF

2019
320 Seiten
Princeton University Press (Verlag)
978-0-691-18963-5 (ISBN)

Infos

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.

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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduce the key figures behind its development.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

Produkt-Details

• Erscheint lt. Verlag: 11.6.2019
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: 5P • Abelian category • abelian group • Abiotic component • Abstract and concrete • Addition • Additive category • Adjoint functors • Adjunction (field theory) • Alexander Grothendieck • algebraic closure • Algebraic cobordism • algebraic cycle • algebraic extension • Algebraic Geometry • algebraic topology • Algebraic topology (object) • Andrei Suslin • Arthur Koestler • Availability • Axiom • Capitalism • centrism • Characteristic class • Charles Darwin • classifying space • Closed set • Codimension • cofibration • cohomology • Cohomology operation • combination • communism • conjecture • Convention (norm) • corollary • Criticism • Darwinism • Determinant • diagram • Diagram (category theory) • Direct limit • ecosystem • Equation • Ethos • exact sequence • Explanation • Factorization • fibration • functor • galois cohomology • Galois extension • Group object • Homology (mathematics) • Homomorphism • Homotopy • Homotopy category • hypersurface • Industry • Inequality (mathematics) • Instance (computer science) • Inverse function • labor relations • Lincoln Steffens • Longevity • Mathematical Induction • Mathematics • Milnor K-theory • minimum wage • Model Category • Module (mathematics) • Monoid • Monomorphism • Morality • Morphism • motivic cohomology • National interest • Natural and legal rights • Natural number • Natural transformation • Normal bundle • Open set • Patriotism • Political Philosophy • Pragmatism • Prediction • Presheaf (category theory) • projective variety • Pushout (category theory) • Quantity • Quillen adjunction • Radicalism (historical) • Rational point • Reactionary • reason • Regular representation • remainder • Retract • rhetoric • Sectarianism • Separable extension • Sheaf (mathematics) • simplicial set • Smooth scheme • Social Darwinism • Social Theory • Sociocultural evolution • Special case • splitting field • SUBGROUP • Subjectivity • Summation • Tangent Space • Teleology • Theorem • theory • Trade Union • Trivial representation • Uncertainty • Vladimir Voevodsky • Weak equivalence (homotopy theory) • World War II • Writing
• ISBN-10: 0-691-18963-3 / 0691189633
• ISBN-13: 978-0-691-18963-5 / 9780691189635