  Aim of this paper is a finer analysis of the group of flat chains with
coefficients in $Z_p$ introduced in a recent paper by Ambrosio-Katz, by taking
quotients of the group of integer rectifiable currents, along the lines of the
the Ziemer and Federer approach. We investigate the typical questions of the
theory of currents, namely rectifiability of the measure-theoretic support and
boundary rectifiability. Our main result can also be interpreted as a closure
theorem for the class of integer rectifiable currents with respect to a (much)
weaker convergence, induced by flat distance mod $p$, and with respect to
weaker mass bounds. A crucial tool in many proofs is the isoperimetric
inequality proved by Ambrosio-Katz with universal constants.
