Cotilting modules and homological ring epimorphisms

We show that every injective homological ring epimorphism f:R--> S where S_R has flat dimension at most one gives rise to a 1-cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and cotilting classes of certain type and in turn, a bijection with a class of smashing localizing subcategories of the derived category of R. Moreover, we obtain that every cotilting class over a valuation domain is a Tor-orthogonal class, hence it is of cocountable type even though in general cotilting classes are not of cofinite type.