{"paper":{"title":"Test ideals via a single alteration and discreteness and rationality of $F$-jumping numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Kevin Tucker, Wenliang Zhang","submitted_at":"2011-07-20T18:41:37Z","abstract_excerpt":"Suppose $(X, \\Delta)$ is a log-$\\bQ$-Gorenstein pair. Recent work of M. Blickle and the first two authors gives a uniform description of the multiplier ideal $\\mJ(X;\\Delta)$ (in characteristic zero) and the test ideal $\\tau(X;\\Delta)$ (in characteristic $p > 0$) via regular alterations. While in general the alteration required depends heavily on $\\Delta$, for a fixed Cartier divisor $D$ on $X$ it is straightforward to find a single alteration (e.g. a log resolution) computing $\\mJ(X; \\Delta + \\lambda D)$ for all $\\lambda \\geq 0$. In this paper, we show the analogous statement in positive chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4059","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"}