{"paper":{"title":"Field extensions, Derivations, and Matroids over Skew Hyperfields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Rudi Pendavingh","submitted_at":"2018-02-07T14:45:57Z","abstract_excerpt":"We show that a field extension $K\\subseteq L$ in positive characteristic $p$ and elements $x_e\\in L$ for $e\\in E$ gives rise to a matroid $M^\\sigma$ on ground set $E$ with coefficients in a certain skew hyperfield $L^\\sigma$. This skew hyperfield $L^\\sigma$ is defined in terms of $L$ and its Frobenius action $\\sigma:x\\mapsto x^p$. The matroid underlying $M^\\sigma$ describes the algebraic dependencies over $K$ among the $x_e\\in L$ , and $M^\\sigma$ itself comprises, for each $m\\in \\mathbb{Z}^E$, the space of $K$-derivations of $K\\left(x_e^{p^{m_e}}: e\\in E\\right)$.\n  The theory of matroid repres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02447","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"}