Cycles, transfers, and motivic homology theories:
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Princeton, N.J.
Princeton University Press
[2000]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 143 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Biographical note: 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 Main description: 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 |
| Beschreibung: | 1 Online-Ressource (288 S.) |
| ISBN: | 9781400837120 |
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| 500 | |a Main description: 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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Datensatz im Suchindex
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| any_adam_object | |
| author | Voevodsky, Vladimir 1966- Suslin, Andrej A. 1950-2018 Friedlander, Eric M. 1944- |
| author_GND | (DE-588)1089287526 (DE-588)1017135770 (DE-588)109731867 |
| author_facet | Voevodsky, Vladimir 1966- Suslin, Andrej A. 1950-2018 Friedlander, Eric M. 1944- |
| author_role | aut aut aut |
| author_sort | Voevodsky, Vladimir 1966- |
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| discipline | Mathematik |
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| spelling | Voevodsky, Vladimir 1966- (DE-588)1089287526 aut Cycles, transfers, and motivic homology theories Vladimir Voevodsky, Andrej Suslin, Eric M. Friedlander Princeton, N.J. Princeton University Press [2000] © 2000 1 Online-Ressource (288 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 143 Biographical note: 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 Main description: 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 Homologietheorie (DE-588)4141714-8 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Motiv Mathematik (DE-588)4197596-0 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s Motiv Mathematik (DE-588)4197596-0 s Homologietheorie (DE-588)4141714-8 s 1\p DE-604 Kohomologie (DE-588)4031700-6 s 2\p DE-604 Suslin, Andrej A. 1950-2018 (DE-588)1017135770 aut Friedlander, Eric M. 1944- (DE-588)109731867 aut Erscheint auch als Druck-Ausgabe 978-0-691-04815-4 Annals of Mathematics Studies number 143 (DE-604)BV040389493 143 http://www.degruyter.com/doi/book/10.1515/9781400837120?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400837120&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Voevodsky, Vladimir 1966- Suslin, Andrej A. 1950-2018 Friedlander, Eric M. 1944- Cycles, transfers, and motivic homology theories Annals of Mathematics Studies Homologietheorie (DE-588)4141714-8 gnd Kohomologie (DE-588)4031700-6 gnd Motiv Mathematik (DE-588)4197596-0 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4031700-6 (DE-588)4197596-0 (DE-588)4141839-6 |
| title | Cycles, transfers, and motivic homology theories |
| title_auth | Cycles, transfers, and motivic homology theories |
| title_exact_search | Cycles, transfers, and motivic homology theories |
| title_full | Cycles, transfers, and motivic homology theories Vladimir Voevodsky, Andrej Suslin, Eric M. Friedlander |
| title_fullStr | Cycles, transfers, and motivic homology theories Vladimir Voevodsky, Andrej Suslin, Eric M. Friedlander |
| title_full_unstemmed | Cycles, transfers, and motivic homology theories Vladimir Voevodsky, Andrej Suslin, Eric M. Friedlander |
| title_short | Cycles, transfers, and motivic homology theories |
| title_sort | cycles transfers and motivic homology theories |
| topic | Homologietheorie (DE-588)4141714-8 gnd Kohomologie (DE-588)4031700-6 gnd Motiv Mathematik (DE-588)4197596-0 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | Homologietheorie Kohomologie Motiv Mathematik Algebraische K-Theorie |
| url | http://www.degruyter.com/doi/book/10.1515/9781400837120?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400837120&searchTitles=true |
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