Abstract: Let X be a separated scheme of finite
type over an algebraically closed field k and let m be a
natural number. By an explicit geometric construction using
torsors we construct a pairing between the first mod m
Suslin homology and the first mod m tame etale cohomology of
X. We show that the induced homomorphism from the mod m
Suslin homology to the abelianized tame fundamental group of
X mod m is surjective. It is an isomorphism of finite
abelian groups if (m, char(k)) = 1, and for general m if
resolution of singularities holds over k. |

pdf-file cft-algclosed-2.pdf.