{"paper":{"title":"On the injective dimension of unit Cartier and Frobenius modules","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Alexandria Wheeler, Daniel Fink, Manuel Blickle, Wenliang Zhang","submitted_at":"2024-12-11T14:43:06Z","abstract_excerpt":"Let $R$ be a regular $F$-finite ring of prime characteristic $p$. We prove that the injective dimension of every unit Frobenius module $M$ in the category of unit Frobenius modules is at most $\\operatorname{dim}(\\operatorname{Supp}_R(M))+1$. We further show that for unit Cartier modules the same bound holds over any noetherian $F$-finite ring $A$ of prime characteristic $p$. This shows that $\\dim A+1$ is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian $F$-finite ring $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08423","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/2412.08423/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"}