Algebraic cobordism:
Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theo...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | Softcover reprint of the hardcover 1. ed. 2007 |
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext |
| Summary: | Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications. |
| Physical Description: | XII, 244 S. graph. Darst. |
| ISBN: | 9783642071911 |
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MARC
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| id | DE-604.BV042564496 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T02:23:14Z |
| institution | BVB |
| isbn | 9783642071911 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027998133 |
| oclc_num | 85804043 |
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| owner | DE-188 |
| owner_facet | DE-188 |
| physical | XII, 244 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Levine, Marc 1952- Verfasser (DE-588)120151499 aut Algebraic cobordism M. Levine ; F. Morel Softcover reprint of the hardcover 1. ed. 2007 Berlin [u.a.] Springer 2007 XII, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications. Cobordismes, Théorie des Cobordismo larpcal Geometria algébrica larpcal Homologie Teoria homológica larpcal Cobordism theory Homology theory Algebraischer Kobordismus (DE-588)4141849-9 gnd rswk-swf Algebraischer Kobordismus (DE-588)4141849-9 s DE-604 Morel, Fabien 1965- Verfasser (DE-588)132679353 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2853644&prov=M&dok_var=1&dok_ext=htm Inhaltstext |
| spellingShingle | Levine, Marc 1952- Morel, Fabien 1965- Algebraic cobordism Cobordismes, Théorie des Cobordismo larpcal Geometria algébrica larpcal Homologie Teoria homológica larpcal Cobordism theory Homology theory Algebraischer Kobordismus (DE-588)4141849-9 gnd |
| subject_GND | (DE-588)4141849-9 |
| title | Algebraic cobordism |
| title_auth | Algebraic cobordism |
| title_exact_search | Algebraic cobordism |
| title_full | Algebraic cobordism M. Levine ; F. Morel |
| title_fullStr | Algebraic cobordism M. Levine ; F. Morel |
| title_full_unstemmed | Algebraic cobordism M. Levine ; F. Morel |
| title_short | Algebraic cobordism |
| title_sort | algebraic cobordism |
| topic | Cobordismes, Théorie des Cobordismo larpcal Geometria algébrica larpcal Homologie Teoria homológica larpcal Cobordism theory Homology theory Algebraischer Kobordismus (DE-588)4141849-9 gnd |
| topic_facet | Cobordismes, Théorie des Cobordismo Geometria algébrica Homologie Teoria homológica Cobordism theory Homology theory Algebraischer Kobordismus |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2853644&prov=M&dok_var=1&dok_ext=htm |
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