Geodesic
Oriented cohomology theories of algebraic varieties II
Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 349-405.

Voir la notice de l'article provenant de la source International Press of Boston

The concept of oriented cohomology theory is well-known in topology. Examples of these kinds of theories are complex cobordism, complex $K$-theory, usual singular cohomology, and Morava $K$-theories. A specific feature of these cohomology theories is the existence of trace operators (or Thom-Gysin operators, or push-forwards) for morphisms of compact complex manifolds. The main aim of the present article is to develop an algebraic version of the concept. Bijective correspondences between orientations, Chern structures, Thom structures and trace structures on a given ring cohomology theory are constructed. The theory is illustrated by singular cohomology, motivic cohomology, algebraic $K$-theory, the algebraic cobordism of Voevodsky and by other examples.
DOI : 10.4310/HHA.2009.v11.n1.a14
Classification : 14F42, 14F43, 55N22
Keywords: motivic cohomology, algebraic cobordism, oriented cohomology theories 
@article{HHA_2009_11_1_a14,
     author = {Ivan Panin},
     title = {Oriented cohomology theories of algebraic varieties {II}},
     journal = {Homology, homotopy, and applications},
     pages = {349--405},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2009},
     doi = {10.4310/HHA.2009.v11.n1.a14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a14/}
}
TY  - JOUR
AU  - Ivan Panin
TI  - Oriented cohomology theories of algebraic varieties II
JO  - Homology, homotopy, and applications
PY  - 2009
SP  - 349
EP  - 405
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a14/
DO  - 10.4310/HHA.2009.v11.n1.a14
LA  - en
ID  - HHA_2009_11_1_a14
ER  - 
%0 Journal Article
%A Ivan Panin
%T Oriented cohomology theories of algebraic varieties II
%J Homology, homotopy, and applications
%D 2009
%P 349-405
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a14/
%R 10.4310/HHA.2009.v11.n1.a14
%G en
%F HHA_2009_11_1_a14
Ivan Panin. Oriented cohomology theories of algebraic varieties II. Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 349-405. doi : 10.4310/HHA.2009.v11.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a14/

Cité par Sources :