{"paper":{"title":"Hilbert irreducibility for algebraic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Borys Kadets, Danny Neftin","submitted_at":"2026-06-09T08:49:35Z","abstract_excerpt":"We study the following problem: given a covering of curves $\\phi\\colon X \\to X_0$ over a number field $k$, and an integer $d$, when is the set \\[\\{p \\in X_0(\\overline{k})|\\ \\mathrm{deg}\\ p = d, \\text{ and the fiber } \\phi^{-1}(p) \\text{ is reducible over } k(p)\\}\\] finite? In case $X$ itself admits infinitely many degree $d$ points, we consider the modified problem where the images of degree $d$ points on $X$ are removed from the set. We prove a number of theorems ensuring a positive answer. As a consequence we show that for a fixed curve $X$ and all sufficiently high-degree indecomposable rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10584","kind":"arxiv","version":1},"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/2606.10584/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"}