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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.02310","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-07T04:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"b7b1f7d935a86b4bb66ef4b185f54cc2f6669f00abe595d75e000f7939358deb","abstract_canon_sha256":"0e3413184c257b9072fcd6b458acc534720ecc63d1fec871ca7fcae4fa4274f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.160816Z","signature_b64":"O139aL3Xd34nuFuBMSR7jnBBu0bzRUaPjVrm3nBZyB9iaOC/UpaeD8TpR8ljAryY0D3EpvkTX5GjTRYGHX5pDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9984c8827a6ce6c00b677a4d978f5abee708a451d6b09d313f14f54c5cc000ae","last_reissued_at":"2026-05-17T23:46:55.160086Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.160086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $I/I^2$. 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