2012/01/14 by Anderson, Benjamin J., Sather-Wagstaff, Sean · 1 citation
#13B40 #13D07 (Primary) 13D02 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1201.3039
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 Exti(S,M) satisfies NAK (e.g. if Exti(S,M) is finitely generated over S) for i=1,...,dimR(M), then Exti(S,M)=0 for all i≠ 0 and M has an S-module structure that is compatible with its R-module structure via f. We provide explicit computations of Ext1(S,M) to indicate how large it can be when M does not have a compatible S-module structure.