  We investigate modules for which vanishing of Tor-modules implies finiteness
of homological dimensions (e.g., projective dimension and G-dimension). In
particular, we answer a question of O. Celikbas and Sather-Wagstaff about
ascent properties of such modules over residually algebraic flat local ring
homomorphisms. To accomplish this, we consider ascent and descent properties
over local ring homomorphisms of finite flat dimension, and for flat extensions
of finite dimensional differential graded algebras.
