  We investigate parametrizations of compactly generated t-structures, or more
generally, t-structures with a definable coaisle, in the unbounded derived
category D(Mod-A) of a ring A. To this end, we provide a construction of
t-structures from chains in the lattice of ring epimorphisms starting in A,
which is a natural extension of the construction of compactly generated
t-structures from chains of subsets of the Zariski spectrum known for the
commutative noetherian case. We also provide constructions of silting and
cosilting objects in D(Mod-A). This leads us to classification results over
some classes of commutative rings and over finite dimensional hereditary
algebras.
