  We show that the Chow group of 0-cycles on a singular projective scheme $X$
over a finite field describes the abelian extensions of its function field
which are unramified over the regular locus of $X$. As a consequence, we obtain
the Bloch-Quillen formula for the Chow group of 0-cycles on such schemes. We
deduce simple proofs of results of Kerz-Saito for a class of surfaces without
any assumption on ${\rm char}(k)$.
