{"paper":{"title":"$p$-bases and differential operators on varieties defined over a non-perfect field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Carlos Abad","submitted_at":"2018-01-25T15:49:13Z","abstract_excerpt":"Let $k$ be a possibly non-perfect field of characteristic $p > 0$. In this work we prove the local existence of absolute $p$-bases for regular algebras of finite type over $k$. Namely, consider a regular variety $Z$ over $k$. Kimura and Niitsuma proved that, for every $\\xi \\in Z$, the local ring $\\mathcal{O}_{Z,\\xi}$ has a $p$-basis over $\\mathcal{O}_{Z,\\xi}^p$. Here we show that, for every $\\xi \\in Z$, there exists an open affine neighborhood of $\\xi$, say $\\xi \\in \\text{Spec}(A) \\subset Z$, so that $A$ admits a $p$-basis over $A^p$.\n  This passage from the local ring to an affine neighborhoo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08458","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":""},"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"}