{"paper":{"title":"Minimal $\\gamma$--sheaves","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Manuel Blickle","submitted_at":"2007-06-27T16:01:36Z","abstract_excerpt":"In this note we show that finitely generated unit $O_X[\\sigma]$--modules for $X$ regular and $F$--finite have a minimal root (in the sense of [Lyubeznik, F-modules] Definition~3.6). This problem was posed by Lyubeznik and answered by himself in the case that $X=\\Spec R$ is a complete local ring.\n  One immediate consequence of this result is that the parameter test module of tight closure theory commutes with localization. As a further application of the methods in this paper we give new proofs of the results on discreteness and rationality of $F$--thresholds [arXiv:0705.1210] and on $D$-module"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4060","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"}