  Rationality results are proved for the ratios of critical values of
Rankin-Selberg L-functions of GL(n) x GL(n') over a totally imaginary field F,
by studying rank-one Eisenstein cohomology for the group GL(N)/F, where N =
n+n', generalizing the methods and results of previous work with Guenter Harder
where the base field was totally real. In contrast to the totally real
situation, the internal structure of the totally imaginary base field has a
delicate effect on the rationality results.
