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Rigidity for orientable functors
- Source :
- Journal of Pure and Applied Algebra. 172:49-77
- Publication Year :
- 2002
- Publisher :
- Elsevier BV, 2002.
-
Abstract
- In the following paper we introduce the notion of orientable functor (orientable cohomology theory) on the category of projective smooth schemes and define a family of transfer maps. Applying this technique, we prove that with finite coefficients orientable cohomology of a projective variety is invariant with respect to the base-change given by an extension of algebraically closed fields. This statement generalizes the classical result of Suslin, concerning algebraic K -theory of algebraically closed fields. Besides K -theory, we treat such examples of orientable functors as etale cohomology, motivic cohomology, algebraic cobordism. We also demonstrate a method to endow algebraic cobordism with multiplicative structure and Chern classes.
- Subjects :
- Discrete mathematics
Pure mathematics
Algebra and Number Theory
Algebraic cobordism
Group cohomology
Étale cohomology
Mathematics::Algebraic Topology
Cohomology
Motivic cohomology
Grothendieck topology
Mathematics::K-Theory and Homology
Ext functor
Equivariant cohomology
Mathematical Physics and Mathematics
Mathematics
Subjects
Details
- ISSN :
- 00224049
- Volume :
- 172
- Database :
- OpenAIRE
- Journal :
- Journal of Pure and Applied Algebra
- Accession number :
- edsair.doi.dedup.....430760f802b3f264958374fd7189c105