Leseprobe
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Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143
Andrei Suslin, Eric M. Friedlander, Vladimir Voevodsky, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles. The material presented provides the foundations for the recent proof of the celebrated "Milnor Conjecture" by Vladimir Voevodsky.
The theory of sheaves of relative cycles is developed in the first paper of this volume. The theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed. The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.
Kundenbewertungen
Topology, Presheaf (category theory), Epimorphism, Triangulated category, Noetherian, Sheaf (mathematics), Zariski topology, Chain complex, Proper morphism, Homotopy category, Type theory, Commutative property, Tensor product, Morphism, Support (mathematics), Affine space, Morphism of schemes, Abelian category, Summation, Monoid, Chow group, Permutation, Embedding, Singular homology, Simplicial set, Vector bundle, Monomorphism, Additive category, Andrei Suslin, Algebraic cycle, Simplicial complex, Zariski's main theorem, Grothendieck topology, Endomorphism, Category of abelian groups, Projective variety, Spectral sequence, Theorem, Homomorphism, Coefficient, Nisnevich topology, Exact sequence, Resolution of singularities, Vladimir Voevodsky, Commutative ring, Mathematical induction, Subcategory, Cohomology, Codimension, Functor, Monoidal category, Homotopy, Adjoint functors, Base change, Milnor K-theory, Pairing, Irreducible component, Quasi-projective variety, Motivic cohomology, Algebraic K-theory, Cokernel, Subgroup, Projective space, Universal coefficient theorem, Picard group, K-theory, Abelian group, Diagram (category theory), Injective sheaf, Smooth scheme