  For certain algebraic Hecke characters chi of an imaginary quadratic field F
we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal
automorphic forms of GL_2/F. By finding congruences between Eisenstein
cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a
lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms
of the special L-value L(0,chi). We further prove that its index is bounded
from above by the order of the Selmer group of the p-adic Galois character
associated to chi^{-1}. This uses the work of R. Taylor et al. on attaching
Galois representations to cuspforms of GL_2/F. Together these results imply a
lower bound for the size of the Selmer group in terms of L(0,chi), coinciding
with the value given by the Bloch-Kato conjecture.
