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arXiv · 2511.01270

A lower bound on the analytic log-canonical threshold over local fields of positive characteristic

Itay Glazer·Yotam I. Hendel
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Abstract

Given a local field $F$ of positive characteristic, an $F$-analytic manifold $X$ and an analytic function $f:X\rightarrow F$, the $F$-analytic log-canonical threshold $\mathrm{lct}_{F}(f;x_{0})$ is the supremum over the values $s\geq0$ such that $\left|f\right|_{F}^{-s}$ is integrable near $x_{0}\in X$. We show that $\mathrm{lct}_{F}(f;x_{0})>0$. Moreover, if $f$ is a regular function on a smooth algebraic $F$-variety, we obtain an effective lower bound $\mathrm{lct}_{F}(f;x_{0})>C$, where $C>0$ is explicit and depends only on the complexity class of $X$ and $f$.

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Itay Glazer, Yotam I. Hendel. 2026-07-31. A lower bound on the analytic log-canonical threshold over local fields of positive characteristic. https://arxiv.org/abs/2511.01270

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