{"paper":{"title":"BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Tatsuki Yamaguchi","submitted_at":"2026-05-21T12:40:30Z","abstract_excerpt":"We introduce a new method for computing plus-pure thresholds, a mixed-characteristic analogue of both log canonical thresholds and $F$-pure thresholds. We obtain some necessary conditions and some sufficient conditions for BCM-regularity of Fermat-type hypersurfaces. We also establish lower bounds for plus-pure thresholds of diagonal hypersurfaces in mixed characteristic. Furthermore, we give bounds for plus-pure thresholds of hypersurfaces in mixed characteristic $(0,2)$ using splitting-order sequences, introduced by Yoshikawa. As an application, we classify BCM-regular diagonal hypersurfaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22419","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22419/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}