  We consider a continuous time Markov chain on a countable state space. We
prove a joint large deviation principle (LDP) of the empirical measure and
current in the limit of large time interval. The proof is based on results on
the joint large deviations of the empirical measure and flow obtained in
\cite{BFG}. By improving such results we also show, under additional
assumptions, that the LDP holds with the strong L^1 topology on the space of
currents. We deduce a general version of the Gallavotti-Cohen (GC) symmetry for
the current field and show that it implies the so-called fluctuation theorem
for the GC functional. We also analyze the large deviation properties of
generalized empirical currents associated to a fundamental basis in the cycle
space, which, as we show, are given by the first class homological coefficients
in the graph underlying the Markov chain. Finally, we discuss in detail some
examples.
