{"paper":{"title":"The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.AC","authors_text":"Angelot Behajaina, Elad Paran, Gil Alon","submitted_at":"2025-08-10T09:17:29Z","abstract_excerpt":"We study zeros of polynomials in the multivariate skew polynomial ring $D[x_1,\\ldots,x_n; \\sigma]$, where $\\sigma$ is an automorphism of a division ring $D$. We prove a generalization of Alon's celebrated Combinatorial Nullstellensatz for such polynomials. In the case where $D$ is a finite field, we prove skew analogues of the Chevalley--Warning theorem, Ax's Lemma, and the weak case of Terjanian's Finitesatz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07257","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/2508.07257/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"}