  We show that the number of supersymmetries of IIB black hole horizons is N=2
N_- + 2 index(D_\lambda), where index(D_\lambda) is the index of the Dirac
operator twisted with the line bundle \lambda^{1/2} of IIB scalars, and N_- is
the dimension of the kernel of a horizon Dirac operator which depends on IIB
fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries.
In addition if the horizons have non-trivial fluxes and N_- is nonzero, then
index(D_\lambda) is non-negative, and the horizons admit an sl(2,R) symmetry
subalgebra. This provides evidence that all such horizons have an AdS/CFT dual.
Furthermore if the orbits of sl(2,R) are two-dimensional, the IIB horizons are
warped products AdS_2 X S.
