We develop a formalism of unit F-modules in the style of Lyubeznik and Emerton-Kisin for rings that have finite F-representation type after localization and completion at every prime ideal. As applications, we show that if R is such a ring then the iterated local cohomology modules H^n₁_I₁ ∘ ⋯ ∘ H^nₛ_Iₛ(R) have finitely many associated primes, and that all local cohomology modules HⁿI(R / gR) have closed support when g is a nonzerodivisor on R.
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Eamon Quinlan-Gallego (2024) studied this question.
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