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• W3105156249 startingPage "1057" @default.
• W3105156249 abstract "The behavior of the Frobenius map is investigated for valuation rings of prime characteristic. We show that valuation rings are always F-pure. We introduce a generalization of the notion of strong F-regularity, which we call F-pure regularity, and show that a valuation ring is F-pure regular if and only if it is Noetherian. For valuations on function fields, we show that the Frobenius map is finite if and only if the valuation is divisorial; in this case the valuation ring is Frobenius split. For Noetherian valuation rings in function fields, we show that the valuation ring is Frobenius split if and only if Frobenius is finite, or equivalently, if and only if the valuation ring is excellent." @default.
• W3105156249 created "2020-11-23" @default.
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• W3105156249 date "2016-07-28" @default.
• W3105156249 modified "2023-10-13" @default.
• W3105156249 title "Frobenius and valuation rings" @default.
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• W3105156249 doi "https://doi.org/10.2140/ant.2016.10.1057" @default.
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