Cargando…
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2007.
|
| Edición: | 1st ed. 2007. |
| Colección: | Springer Monographs in Mathematics,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-540-36824-3 | ||
| 003 | DE-He213 | ||
| 005 | 20220112235132.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2007 gw | s |||| 0|eng d | ||
| 020 | |a 9783540368243 |9 978-3-540-36824-3 | ||
| 024 | 7 | |a 10.1007/3-540-36824-8 |2 doi | |
| 050 | 4 | |a QA612-612.8 | |
| 072 | 7 | |a PBPD |2 bicssc | |
| 072 | 7 | |a MAT038000 |2 bisacsh | |
| 072 | 7 | |a PBPD |2 thema | |
| 082 | 0 | 4 | |a 514.2 |2 23 |
| 100 | 1 | |a Levine, Marc. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Algebraic Cobordism |h [electronic resource] / |c by Marc Levine, Fabien Morel. |
| 250 | |a 1st ed. 2007. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2007. | |
| 300 | |a XII, 246 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Algebraic topology. | |
| 650 | 0 | |a Topology. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 0 | |a Commutative algebra. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a K-theory. | |
| 650 | 1 | 4 | |a Algebraic Topology. |
| 650 | 2 | 4 | |a Topology. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 650 | 2 | 4 | |a Commutative Rings and Algebras. |
| 650 | 2 | 4 | |a K-Theory. |
| 700 | 1 | |a Morel, Fabien. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642071911 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540827214 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540368229 |
| 830 | 0 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/3-540-36824-8 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||