  We map out the detuning-magnetization phase diagram for a ``magnetized''
(unequal number of atoms in two pairing hyperfine states) gas of fermionic
atoms interacting via an s-wave Feshbach resonance (FR). For large positive FR
detuning a normal magnetized Fermi gas is stable above an exponentially small
value of the population difference. Below this critical value the phase diagram
is dominated by coexistence of a magnetized normal gas and a singlet paired
superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover
with reduced detuning. On the BCS side of strongly overlapping Cooper pairs, a
sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized
phase intervenes between the phase separated and normal states. In contrast,
for large negative detuning a uniform, polarized superfluid, that is a coherent
mixture of singlet Bose-Einstein-condensed molecules and fully magnetized
single-species Fermi-sea, is a stable ground state.
