{"paper":{"title":"A lower bound on the analytic log-canonical threshold over local fields of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Itay Glazer, Yotam I. Hendel","submitted_at":"2025-11-03T06:45:40Z","abstract_excerpt":"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 $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.01270","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.01270/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}