%0 Journal Article
%T NAK for Ext and Ascent of module structures
%A Benjamin J. Anderson
%A Sean Sather-Wagstaff
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1201.3039v2