Geodesic
Projective bundle theorem in homology theories with Chern structure
Documenta mathematica, Tome 9 (2004), pp. 487-497
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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.
DOI : 10.4171/dm/175
Mots-clés : (Co)homology theory, Chern structure, projective bundle, algebraic variety 
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     author = {Alexander Nenashev},
     title = {Projective bundle theorem in homology theories with {Chern} structure},
     journal = {Documenta mathematica},
     pages = {487--497},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/175},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/175/}
}
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Alexander Nenashev. Projective bundle theorem in homology theories with Chern structure. Documenta mathematica, Tome 9 (2004), pp. 487-497. doi: 10.4171/dm/175

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