{"paper":{"title":"On asymptotic vanishing behavior of local cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hailong Dao, Jonathan Monta\\~no","submitted_at":"2018-09-07T04:47:55Z","abstract_excerpt":"Let $R$ be a standard graded algebra over a field $k$, with irrelevant maximal ideal $\\fm$, and $I$ a homogeneous $R$-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules $\\{\\HH{i}{\\fm}{R/I^n}\\}_{n\\in \\NN}$ for $i<\\dim R/I$. We show that, when $\\chara k= 0$, $R/I$ is Cohen-Macaulay, and $I$ is a complete intersection locally on $\\Spec R \\setminus\\{\\fm\\}$, the lowest degrees of the modules $\\{\\HH{i}{\\fm}{R/I^n}\\}_{n\\in \\NN}$ are bounded by a linear function whose slope is controlled by the generating degrees of the dual of $I/I^2$. Our resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02310","kind":"arxiv","version":2},"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"}