  We perform a theoretical study of a fermionic gas with two hyperfine states
confined to an optical lattice. We derive a generic state diagram as a function
of interaction strength, particle number, and confining potential. We discuss
the central density, the double occupancy and their derivatives as probes for
the Mott state, connecting our findings to the recent experiment of J\"ordens
et al. Using entropic arguments we compare two different strategies to reach
the antiferromagnetic state in the presence of a trapping potential.
