This is a report of an ongoing work with K. Prasanna. Let p be a prime; inspired by an earlier work by E. Urban and myself which treated the case of the quadratic base change for GL_2, we formulate a conjecture (and establish part of it), in the case of the transfer from GSp(4) to GL(4),
of a cohomological cuspidal representation \pi, relating the integral periods of \pi and those of its transfer. The proof involves special values of adjoint automorphic L functions and their interpretation as congruence numbers. It seems it can be generalized to several other transfers. It has also consequences for the Bloch-Kato conjecture at p.