论文标题
稳定性和f线索的变形
Stability and deformation of F-singularities
论文作者
论文摘要
We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a sufficiently small $\mathfrak{m}$-adic neighborhood of $ x $。我们表明，$ \ mathfrak {m} $ - ADIC稳定性具有完全一般性的F理性，以及在某些假设下具有F formentitive，f indentitive，f indentivity，f indectivity，f purity and f-Partigation。我们表明，强大的F型和F纯度通常不稳定。此外，我们在稳定与变形现象之间表现出牢固的联系，这具有很大的一般性。
We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a sufficiently small $\mathfrak{m}$-adic neighborhood of $x$. We show that $\mathfrak{m}$-adic stability holds for F-rationality in full generality, and for F-injectivity, F-purity and strong F-regularity under certain assumptions. We show that strong F-regularity and F-purity are not stable in general. Moreover, we exhibit strong connections between stability and deformation phenomena, which hold in great generality.
