Chargement en cours…

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...

Description complète

Détails bibliographiques
Cote:Libro Electrónico
Auteurs principaux: Levine, Marc (Auteur), Morel, Fabien (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2007.
Édition:1st ed. 2007.
Collection:Springer Monographs in Mathematics,
Sujets:
Accès en ligne:Texto Completo
Table des matières:
  • 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.