  We show for a ring R of weak global dimension at most one that there is a
bijection between the smashing subcategories of its derived category and the
equivalence classes of homological epimorphisms starting in R. If, moreover, R
is commutative, we prove that the compactly generated localizing subcategories
correspond precisely to flat epimorphisms. We also classify smashing
localizations of the derived category of any valuation domain, and provide an
easy criterion for the Telescope Conjecture (TC) for any commutative ring of
weak global dimension at most one. As a consequence, we show that the TC holds
for any commutative von Neumann regular ring R, and it holds precisely for
those Pr\"ufer domains which are strongly discrete.

Commutative Algebra;Algebraic Topology;Category Theory