Algebraic Cobordism / Levine, Marc (2007)  

Público ISBD Título : Algebraic Cobordism Tipo de documento: documento electrónico Autores: Levine, Marc ; SpringerLink (Online service) ; Morel, Fabien Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XII, 246 p Il.: online resource ISBN/ISSN/DL: 978-3-540-36824-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Commutative  algebra  rings  K-theory  Topology  topology  Geometry  Rings  and  Algebras  K-Theory Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: 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 En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628 Algebraic Cobordism [documento electrónico] / Levine, Marc ; SpringerLink (Online service) ; Morel, Fabien . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XII, 246 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) . ISBN : 978-3-540-36824-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Commutative  algebra  rings  K-theory  Topology  topology  Geometry  Rings  and  Algebras  K-Theory Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: 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 En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628

Ejemplares

Signatura	Medio	Ubicación	Sub-localización	Sección	Estado
ningún ejemplar

Motivic Homotopy Theory / SpringerLink (Online service) ; Dundas, Bjørn Ian ; Levine, Marc ; Østvær, Paul Arne ; Röndigs, Oliver ; Voevodsky, Vladimir (2007)  

Público ISBD Título : Motivic Homotopy Theory : Lectures at a Summer School in Nordfjordeid, Norway, August 2002 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Dundas, Bjørn Ian ; Levine, Marc ; Østvær, Paul Arne ; Röndigs, Oliver ; Voevodsky, Vladimir Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 226 p Il.: online resource ISBN/ISSN/DL: 978-3-540-45897-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Group  theory  topology  Theory  and  Generalizations  Topology  Geometry Clasificación: 51 Matemáticas Nota de contenido: Prerequisites in Algebraic Topology the Nordfjordeid Summer School on Motivic Homotopy Theory -- Basic Properties and Examples -- Deeper Structure: Simplicial Sets -- Model Categories -- Motivic Spaces and Spectra -- Background from Algebraic Geometry -- Elementary Algebraic Geometry -- Sheaves for a Grothendieck Topology -- Voevodsky’s Nordfjordeid Lectures: Motivic Homotopy Theory -- Voevodsky’s Nordfjordeid Lectures: Motivic Homotopy Theory En línea: http://dx.doi.org/10.1007/978-3-540-45897-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34634 Motivic Homotopy Theory : Lectures at a Summer School in Nordfjordeid, Norway, August 2002 [documento electrónico] / SpringerLink (Online service) ; Dundas, Bjørn Ian ; Levine, Marc ; Østvær, Paul Arne ; Röndigs, Oliver ; Voevodsky, Vladimir . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - X, 226 p : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-3-540-45897-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Group  theory  topology  Theory  and  Generalizations  Topology  Geometry Clasificación: 51 Matemáticas Nota de contenido: Prerequisites in Algebraic Topology the Nordfjordeid Summer School on Motivic Homotopy Theory -- Basic Properties and Examples -- Deeper Structure: Simplicial Sets -- Model Categories -- Motivic Spaces and Spectra -- Background from Algebraic Geometry -- Elementary Algebraic Geometry -- Sheaves for a Grothendieck Topology -- Voevodsky’s Nordfjordeid Lectures: Motivic Homotopy Theory -- Voevodsky’s Nordfjordeid Lectures: Motivic Homotopy Theory En línea: http://dx.doi.org/10.1007/978-3-540-45897-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34634

Ejemplares

Signatura	Medio	Ubicación	Sub-localización	Sección	Estado
ningún ejemplar