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- W4226085893 abstract "The containment problem for symbolic and ordinary powers of ideals asks for what values of a and b we have $$I^{(a)} subseteq I^b$$ . Over a regular ring, a result by Ein–Lazarsfeld–Smith, Hochster–Huneke, and Ma–Schwede partially answers this question, but the containments it provides are not always best possible. In particular, a tighter containment conjectured by Harbourne has been shown to hold for interesting classes of ideals—although it does not hold in general. In this paper, we develop a Fedder (respectively, Glassbrenner) type criterion for F-purity (respectively, strong F-regularity) for ideals of finite projective dimension over F-finite Gorenstein rings and use our criteria to extend the prime characteristic results of Grifo–Huneke to singular ambient rings. For ideals of infinite projective dimension, we prove that a variation of the containment still holds, in the spirit of work by Hochster–Huneke and Takagi." @default.
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- W4226085893 date "2022-01-20" @default.
- W4226085893 modified "2023-10-13" @default.
- W4226085893 title "Symbolic power containments in singular rings in positive characteristic" @default.
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- W4226085893 doi "https://doi.org/10.1007/s00229-021-01359-7" @default.
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