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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 17/2002

I. Panin
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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.

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