  We discuss Suslin's singular homology and cohomology. In the first half we
examine the p-part in characteristic p, and the situation over
non-algebraically closed fields. In the second half we focus on finite base
fields. We study finite generation properties, and give a modified definition
which behaves like a homology theory: in degree zero it is a copy of Z for each
connected component, in degree one it is related to the abelianized (tame)
fundamental group, even for singular schemes, and it is expected to be finitely
generated in general.
