  We investigate the interplay between properties of Ext modules and ascent of
module structures along local ring homomorphisms. Specifically, let f: (R,m,k)
-> (S,mS,k) be a flat local ring homomorphism. We show that if M is a finitely
generated R-module such that Ext^i(S,M) satisfies NAK (e.g. if Ext^i(S,M) is
finitely generated over S) for i=1,...,dim_R(M), then Ext^i(S,M)=0 for all
i\neq 0 and M has an S-module structure that is compatible with its R-module
structure via f. We provide explicit computations of Ext^1(S,M) to indicate how
large it can be when M does not have a compatible S-module structure.
