Steklov Institute of Mathematics at St.Petersburg

PREPRINT 17/2002

PUSH-FORWARDS IN ORIENTED COHOMOLOGY THEORIES OF ALGEBRAIC VARIETIES: II

This preprint was accepted October 10, 2002
Contact: I. A. Panin

ABSTRACT:
This preprint contains proofs of the results anounced in 
I. Panin, A. Smirnov, ``Push-forwards in oriented Cohomology
Theories of Algebraic Varieties,''
 http://www.math.uiuc.edu/K-theory/0459/2000,
in the part concerning the construction of push-forwards for
an oriented cohomology theory. One-to-one
correspondences are constructed 
between orientations, Chern structures, Thom structures
and integrations on a given ring cohomology theory.  
The theory is illustrated by motivic cohomology, algebraic
K-theory, algebraic cobordism theory and by other examples.
Other terms often used in the literature for push-forwards are Gysin 
homomorphisms, trace homomorphisms, corestriction homomorphisms, transfers.