{"paper":{"title":"A note on the growth of regularity with respect to Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Wenliang Zhang","submitted_at":"2015-11-30T21:31:22Z","abstract_excerpt":"Let $R=k[x_1,\\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\\dots,x_n)$ by $\\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00049","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"}