The Frobenius conjecture for biseparable corings

Let $A$ be a ring and let ${\mathcal C}$ be an $A$-coring, meaning an $A$-bimodule equipped with counit and comultiplication maps satisfying the coring axioms. The coring ${\mathcal C}$ is biseparable when ${\mathcal C}_A$ and ${}_A{\mathcal C}$ are finitely generated projective and ${\mathcal C}$ is both cosplit and coseparable. Frobenius conjecture. Every biseparable $A$-coring ${\mathcal C}$ is Frobenius, meaning that the forgetful functor $F:{\bf M}^{\mathcal C}\to{\bf M}_A$ is a Frobenius functor, equivalently that $-\otimes_A{\mathcal C}$ is both a left and a right adjoint of $F$. This asks whether the finiteness and separability conditions defining biseparable corings force the associated comodule forgetful functor to have coinciding adjoints; the supplied text does not indicate whether the conjecture has been resolved.