  In this paper we reinterpret the Poisson structure of the Hitchin-type system
in cohomological terms. The principal ingredient of a new interpretation in the
case of the Beauville system is the meromorphic cohomology of the spectral
curve, and the main result is the identification of the Riemann bilinear form
and the symplectic structure of the model. Eventual perspectives of this
approach lie in the quantization domain.
