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Cover: 9783642071911 | Algebraic Cobordism | Fabien Morel (u. a.) | Taschenbuch | Paperback
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Algebraic Cobordism
Taschenbuch von Fabien Morel (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
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.
Inhaltsverzeichnis
Cobordism and oriented cohomology.- The definition of algebraic cobordism.- Fundamental properties of algebraic cobordism.- Algebraic cobordism and the Lazard ring.- Oriented Borel-Moore homology.- Functoriality.- The universality of algebraic cobordism.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Monographs in Mathematics
Inhalt: xii
246 S.
ISBN-13: 9783642071911
ISBN-10: 3642071910
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Morel, Fabien
Levine, Marc
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 235 x 155 x 15 mm
Von/Mit: Fabien Morel (u. a.)
Erscheinungsdatum: 30.11.2010
Gewicht: 0,4 kg
Artikel-ID: 107175595
Zusammenfassung
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.
Inhaltsverzeichnis
Cobordism and oriented cohomology.- The definition of algebraic cobordism.- Fundamental properties of algebraic cobordism.- Algebraic cobordism and the Lazard ring.- Oriented Borel-Moore homology.- Functoriality.- The universality of algebraic cobordism.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Monographs in Mathematics
Inhalt: xii
246 S.
ISBN-13: 9783642071911
ISBN-10: 3642071910
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Morel, Fabien
Levine, Marc
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 235 x 155 x 15 mm
Von/Mit: Fabien Morel (u. a.)
Erscheinungsdatum: 30.11.2010
Gewicht: 0,4 kg
Artikel-ID: 107175595
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