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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| Auteurs principaux: | , , |
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| 格式: | Livre numérique |
| 語言: | Anglais |
| 出版: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2007. |
| 叢編: | Springer Monographs in Mathematics
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| 主題: | |
| 在線閱讀: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 提示: |
L'impression du document génère 251 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Berlin ; Heidelberg ; New York : Springer , cop.2007 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Algebraic cobordism, M. Levine, F. Morel, Berlin, Springer, 2007, 1 vol. (XII-244 p.), Springer monographs in mathematics, 978-3-540-36822-9 • Algebraic Cobordism, Texte imprimé, 9783642071911 • Algebraic Cobordism, Texte imprimé, 9783540827214 • Algebraic cobordism, M. Levine, F. Morel, Berlin, Springer, 2007, 1 vol. (XII-244 p.), Springer monographs in mathematics, 978-3-540-36822-9 |
書本目錄:
- Introduction I. Cobordism and oriented cohomology 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications Appendix A: Resolution of singularities References Index Glossary of Notation