  The aim of this paper is to show that Besser syntomic cohomology is
representable by a rational ring spectrum in the motivic homotopical sense. In
fact, extending previous constructions, we exhibit a simple representability
criterion and we apply it to several cohomologies in order to get our central
result. This theorem gives new results for syntomic cohomology such as
h-descent and the compatibility of cycle classes with Gysin morphisms. Along
the way, we prove that motivic ring spectra induces a complete Bloch-Ogus
cohomological formalism and even more. Finally, following a general motivic
homotopical philosophy, we exhibit a natural notion of syntomic coefficients.
