Algebraically constructible homology
by
Helene Pennaneac'h
University of Rennes

For a real algebraic variety, we define semialgebraic chains using the real spectrum of the fields of rational funtions of subvarieties, oriented by Kahler forms of higher dimension. We also construct a boundary for these chains using discrete valuations of the fields of rational functions."Algebraic" chains are distinguished among semialgebraic chains by a fan criterion ; they have the property that half their boundary is still algebraic. This allows us to construct many homology groups.

Date received: April 28, 1999