Projective Bundle Theorem in Homology Theories with Chern Structure

Panin and Smirnov deduced the existence of push-forwards, along projective morphisms, in a cohomology theory with cup products, from the assumption that the theory is endowed with an extra structure called orientation. A part of their work is a proof of the Projective Bundle Theorem in cohomology based on the assumption that we have the first Chern class for line bundles. In some examples we have to consider a pair of theories, cohomology and homology, related by a cap product. It would be useful to construct transfer maps (pull-backs) along projective morphisms in homology in such a situation under similar assumptions. In this note we perform the projective bundle theorem part of this project in homology.

2000 Mathematics Subject Classification:

Keywords and Phrases: (Co)homology theory, Chern structure, projective bundle, algebraic variety

Full text: dvi.gz 22 k, dvi 55 k, ps.gz 544 k, pdf 133 k.

Home Page of DOCUMENTA MATHEMATICA