  We consider interacting fermions in a magnetic field on a two-dimensional
lattice with the periodic boundary conditions. In order to measure the Hall
current, we apply an electric potential with a compact support. Then, due to
the Lorentz force, the Hall current appears along the equipotential line.
Introducing a local current operator at the edge of the potential, we derive
the Hall conductance as a linear response coefficient. For a wide class of the
models, we prove that if there exists a spectral gap above the degenerate
ground state, then the Hall conductance of the ground state is fractionally
quantized without averaging over the fluxes. This is an extension of the
topological argument for the integrally quantized Hall conductance in
noninteracting fermion systems on lattices.
