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The Norm Residue Theorem in Motivic Cohomology

(AMS-200)

Christian Haesemeyer, Charles A. Weibel

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ca. 77,99
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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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 The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development.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

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Schlagwörter

Additive category, Axiom, Algebraic cycle, Theorem, Algebraic topology, Conjecture, Abelian group, Inverse function, Trivial representation, Andrei Suslin, Remainder, Weak equivalence (homotopy theory), Exact sequence, Morphism, Galois cohomology, Rational point, Algebraic extension, Milnor K-theory, Galois extension, Group object, Smooth scheme, Vladimir Voevodsky, Summation, Homotopy category, Retract, Corollary, Model category, Direct limit, Diagram (category theory), Closed set, Pushout (category theory), Algebraic cobordism, Cofibration, Mathematics, Motivic cohomology, Tangent space, Quillen adjunction, Sheaf (mathematics), Functor, Addition, Monoid, Monomorphism, Algebraic closure, Presheaf (category theory), Adjoint functors, Characteristic class, Separable extension, Cohomology operation, Homotopy, Factorization, Fibration, Subgroup, Mathematical induction, Open set, Quantity, Alexander Grothendieck, Classifying space, Hypersurface, Module (mathematics), Cohomology, Codimension, Regular representation, Homology (mathematics), Special case, Normal bundle, 5P, Algebraic geometry, Natural number