{"paper":{"title":"On the upper semi-continuity of HSL numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Serena Murru","submitted_at":"2013-02-05T17:11:37Z","abstract_excerpt":"Let $B$ be an affine Cohen-Macaulay algebra over a field of characteristic $p$. For every prime ideal $\\mathfrak{p}\\subset B$, let $\\text{H}_\\mathfrak{p}$ denote $H^{\\dim B_\\mathfrak{p}}_{\\mathfrak{p} B_\\mathfrak{p}}\\left( \\widehat{B_\\mathfrak{p}} \\right)$. Each such $\\text{H}_\\mathfrak{p}$ is an Artinian module endowed with a natural Frobenius map $\\Theta$ and if $\\text{Nil}(\\text{H}_\\mathfrak{p})$ denotes the set of all elements in $\\text{H}_\\mathfrak{p}$ killed by some power of $\\Theta$ then a theorem by Hartshorne-Speiser and Lyubeznik shows that there exists an $e\\geq 0$ such that $\\Theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1124","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"}