{"paper":{"title":"Extending weakly polynomial functions from high rank varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"David Kazhdan, Tamar Ziegler","submitted_at":"2018-08-28T17:54:48Z","abstract_excerpt":"Let $k$ be a field, $V$ a $k$-vector space and $X$ be a subset of $V $. A function $f:X\\to k$ is weakly polynomial of degree $\\leq a$, if the restriction of $f$ on any affine subspace $L\\subset X$ is a polynomial of degree $\\leq a$. In this paper we consider the case when $X= \\mathbb X (k)$ where $\\mathbb X$ is a complete intersection of bounded codimension defined by a high rank polynomials of degrees $d, char(k)=0$ or $char (k)>d$ and either $k$ is algebraically closed, or $k=\\mathbb F _q,q>ad$. We show that under these assumptions any $k$-valued weakly polynomial function of degree $ \\leq a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09439","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}