Cycles, Transfers, and Motivic Homology Theories
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A01=Andrei Suslin
A01=Eric M. Friedlander
A01=Vladimir Voevodsky
Abelian category
Abelian group
Additive category
Adjoint functors
Affine space
Algebraic cycle
Algebraic K-theory
Andrei Suslin
Author_Andrei Suslin
Author_Eric M. Friedlander
Author_Vladimir Voevodsky
Base change
Category of abelian groups
Category=PBF
Chain complex
Chow group
Codimension
Coefficient
Cohomology
Cokernel
Commutative property
Commutative ring
Diagram (category theory)
Embedding
Endomorphism
Epimorphism
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact sequence
Functor
Grothendieck topology
Homomorphism
Homotopy
Homotopy category
Injective sheaf
Irreducible component
K-theory
Mathematical induction
Milnor K-theory
Monoid
Monoidal category
Monomorphism
Morphism
Morphism of schemes
Motivic cohomology
Nisnevich topology
Noetherian
Pairing
Permutation
Picard group
Presheaf (category theory)
Projective space
Projective variety
Proper morphism
Quasi-projective variety
Resolution of singularities
Sheaf (mathematics)
Simplicial complex
Simplicial set
Singular homology
Smooth scheme
Spectral sequence
Subcategory
Subgroup
Summation
Support (mathematics)
Tensor product
Theorem
Topology
Triangulated category
Type theory
Universal coefficient theorem
Vector bundle
Vladimir Voevodsky
Zariski topology
Zariski's main theorem
Product details
- ISBN 9780691048154
- Weight: 397g
- Dimensions: 152 x 235mm
- Publication Date: 24 Apr 2000
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Vladimir Voeodsky is at the Institute for Advanced Study, Princeton. Andrei Suslin and Eric M. Friedlander teach in the Department of Mathematics at Northwestern University.
