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Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143
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Cycles, Transfers, and Motivic Homology Theories. (AM-143), Volume 143

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.

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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.

Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 256
ISBN-13: 9780691048154
Indbinding: Paperback
Udgave:
ISBN-10: 0691048150
Kategori: Algebra
Udg. Dato: 24 apr 2000
Længde: 16mm
Bredde: 234mm
Højde: 156mm
Oplagsdato: 24 apr 2000
Forfatter(e) Vladimir Voevodsky, Andrei Suslin, Eric M. Friedlander


Kategori Algebra


Sprog Engelsk


Indbinding Paperback


Sider 256


Udgave


Længde 16mm


Bredde 234mm


Højde 156mm


Udg. Dato 24 apr 2000


Oplagsdato 24 apr 2000

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