# Fiber-full modules and a local freeness criterion for local cohomology modules

@inproceedings{CidRuiz2021FiberfullMA, title={Fiber-full modules and a local freeness criterion for local cohomology modules}, author={Yairon Cid-Ruiz}, year={2021} }

Let R be a finitely generated positively graded algebra over a Noetherian local ring B, and m = [R]+ be the graded irrelevant ideal of R. We provide a local criterion characterizing the B-freeness of all the local cohomology modules Hm(M) of a finitely generated graded R-module M. We show that fiberfull modules are exactly the ones that satisfy this criterion. When we change B by an arbitrary Noetherian ring A, we study the fiber-full locus of a module in Spec(A): we show that the fiber-full… Expand

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