### Singular homology of abstract algebraic varieties, by Andrei Suslin and Vladimir Voevodsky

We define for any algebraic variety X over a field k a complex of abelian
groups whose homology groups are called algebraic singular homology groups of
X. This definition was suggested by the first author in 1986 and two
conjectures were made relating these groups to higher Chow groups (for
integral coefficients) and to etale cohomology (for finite coefficients). In
this paper we prove the second conjecture. There is an appendix which
contains a brief summary of main properties of h- and qfh-topologies which
are used in the proof.
After this paper was written, the first conjecture was proved by Suslin. See
"Higher Chow groups and etale cohomology".

Andrei Suslin <suslin@lomi.spb.su>

Vladimir Voevodsky <vladimir@math.harvard.edu>