  We classify all compactly generated t-structures in the unbounded derived
category of an arbitrary commutative ring, generalizing the result of [ATLJS10]
for noetherian rings. More specifically, we establish a bijective
correspondence between the compactly generated t-structures and infinite
filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that
in the case of a commutative noetherian ring, any bounded below homotopically
smashing t-structure is compactly generated. As a consequence, all cosilting
complexes are classified up to equivalence.
