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arXiv · 1201.3039

NAK for Ext and Ascent of module structures

Benjamin J. Anderson·Sean Sather-Wagstaff
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Abstract

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.

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Benjamin J. Anderson, Sean Sather-Wagstaff. 2012-05-14. NAK for Ext and Ascent of module structures. https://arxiv.org/abs/1201.3039

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