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- W2892776166 abstract "We utilize recent results of Andr'e 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.
- W2892776166 created "2018-10-05" @default.
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- W2892776166 date "2018-06-25" @default.
- W2892776166 modified "2023-09-24" @default.
- W2892776166 title "Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras" @default.
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- W2892776166 doi "https://doi.org/10.48550/arxiv.1806.09567" @default.
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