Abstract
Let be a complete commutative Noetherian local ring, I an ideal of R, M an R-module (not necessarily I-torsion) and N a finitely generated R-module with . It is shown that if M is I-ETH-cominimax (i.e. is minimax (or Matlis reflexive), for all ) and or more generally , then the R-module is finitely generated, for all . As an application to local cohomology, let be a system of ideals of R and , if (e.g., ) for all , then the R-modules are finitely generated, for all and . Similar results are true for local cohomology defined by a pair of ideals and ordinary local cohomology modules.
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