Traces in oriented homology theories of algebraic varieties, by Konstantin I. Pimenov

The present preprint is the first one in a short series of preprints. The main aim of this series is to give a proof of "the only non-trivial result on algebraic cobordism" stated by V. Voevodsky in his preprint on Milnor Conjecture. In this preprint we introduce the notion of oriented homology theory on smooth algebraic varieties following the strategy suggested by Panin. We consider three structures on a homology theory: an orientation, a Thom structure and a Chern structure. We describe relations of these structures to each other. These should be considered as a preliminary to construct trace structure on an oriented homology theory. The proper construction of the trace structure is postponed to the next preprint.

Konstantin I. Pimenov <>