通过弗罗本尼斯图和 f-nilpotent 奇点计算几何分支

Pub Date : 2024-02-27 DOI:10.1017/nmj.2024.4

HAILONG DAO, KYLE MADDOX, VAIBHAV PANDEY

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引用次数: 0

摘要

我们给出了一个明确的公式，利用紧闭理论计算正特征曲线的几何分支数。这个公式很容易说明，具有单一几何分支的特性是 F-nilpotent 曲线的特征。此外，我们还证明了一个还原的局部 F-nilpotent 环具有单一几何分支；特别是，它是一个域。最后，我们研究了沿纯不可分割环扩展的弗罗贝尼斯检验指数的不等式，并将其应用于 F-nilpotent 仿射半群环。

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COUNTING GEOMETRIC BRANCHES VIA THE FROBENIUS MAP AND F-NILPOTENT SINGULARITIES

We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes F-nilpotent curves. Further, we show that a reduced, local F-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities of Frobenius test exponents along purely inseparable ring extensions with applications to F-nilpotent affine semigroup rings.

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