  We study superfluid and Mott insulator phases of cold spin-1 Bose atoms with
antiferromagnetic interactions in an optical lattice, including a usual polar
condensate phase, a condensate of singlet pairs, a crystal spin nematic phase,
and a spin singlet crystal phase. We suggest a possibility of exotic
fractionalized phases of spinor BEC and discuss them in the language of
topological defect condensation and $Z_2$ lattice gauge theory.
