Critical values of automorphic L-functions for GL(r) x GL(r)

We compute, up to an element of a fixed number field, the critical values of the L-function of a pair of automorphic, cuspidal, cohomological representations of any GL(r). The result is expressed as a product of cohomological periods divided by an archimedean integral. The main tool used is the rationality of the cohomology of the three representations involved in the Rankin-Selberg integral. As an intermediate step, we also obtained the rationality of the Eisenstein cohomology.