The Resource Algebraic cobordism, M. Levine, F. Morel, (electronic resource)

Algebraic cobordism, M. Levine, F. Morel, (electronic resource)

Label
Algebraic cobordism
Title
Algebraic cobordism
Statement of responsibility
M. Levine, F. Morel
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
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
Member of
Is Subseries of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1952-
http://library.link/vocab/creatorName
Levine, Marc
Dewey number
514/.72
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA612.66
LC item number
.L48 2007
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Morel, Fabien
Series statement
Springer monographs in mathematics,
http://library.link/vocab/subjectName
  • Cobordism theory
  • Homology theory
Label
Algebraic cobordism, M. Levine, F. Morel, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [237]-238) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Extent
1 online resource (254 p.)
Form of item
online
Isbn
9783540368243
Media category
computer
Media type code
  • c
Other control number
10.1007/3-540-36824-8
Specific material designation
remote
System control number
  • (CKB)1000000000282707
  • (EBL)323022
  • (OCoLC)185022118
  • (SSID)ssj0000101019
  • (PQKBManifestationID)11124516
  • (PQKBTitleCode)TC0000101019
  • (PQKBWorkID)10037263
  • (PQKB)10111334
  • (DE-He213)978-3-540-36824-3
  • (MiAaPQ)EBC323022
  • (EXLCZ)991000000000282707
Label
Algebraic cobordism, M. Levine, F. Morel, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [237]-238) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Extent
1 online resource (254 p.)
Form of item
online
Isbn
9783540368243
Media category
computer
Media type code
  • c
Other control number
10.1007/3-540-36824-8
Specific material designation
remote
System control number
  • (CKB)1000000000282707
  • (EBL)323022
  • (OCoLC)185022118
  • (SSID)ssj0000101019
  • (PQKBManifestationID)11124516
  • (PQKBTitleCode)TC0000101019
  • (PQKBWorkID)10037263
  • (PQKB)10111334
  • (DE-He213)978-3-540-36824-3
  • (MiAaPQ)EBC323022
  • (EXLCZ)991000000000282707

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