Doc. Math. (Bielefeld) Extra Vol. Andrei A. Suslin's Sixtieth Birthday, 223-249 (2010)
We study properties of Suslin homology and cohomology over non-algebraically closed base fields, and their $p$-part in characteristic $p$. In the second half we focus on finite fields, and consider finite generation questions and connections to tamely ramified class field theory.