A locally F-finite Noetherian domain that is not F-finite

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.Comment: Comments are welcome

Cohen Macaulay fibres of a morphism

We present the main results about morphisms whose fibres are Cohen-Macaulay and about rings having Cohen-Macaulay formal fibers. We give new proofs for the localization theorems for morphisms with Cohen-Macaulay or (Sn) fibres and we point out some open questions in this direction