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- W3198333885 abstract "We utilize recent results of André and Gabber on the existence of weakly functorial, integral perfectoid big Cohen–Macaulay (BCM) algebras to study singularities of local rings in mixed characteristic. In particular, we introduce a mixed characteristic BCM-variant of rational/F-rational singularities, of log terminal/F-regular singularities, and of multiplier/test ideals of divisor pairs. We prove a number of results about these objects including a restriction theorem for perfectoid BCM multiplier/test ideals and deformation statements for perfectoid BCM-regular and BCM-rational singularities. As an application, we obtain results on the behavior of F-regular and F-rational singularities in arithmetic families." @default.
- W3198333885 created "2021-09-13" @default.
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- W3198333885 date "2021-09-15" @default.
- W3198333885 modified "2023-10-02" @default.
- W3198333885 title "Singularities in mixed characteristic via perfectoid big Cohen–Macaulay algebras" @default.
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- W3198333885 doi "https://doi.org/10.1215/00127094-2020-0082" @default.
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