{"paper":{"title":"Coherent-Constructible Correspondence for Toric Fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.AG","authors_text":"Pyongwon Suh, Yuxuan Hu","submitted_at":"2023-04-03T09:20:13Z","abstract_excerpt":"Let $\\Sigma$ be a fan inside the lattice $\\mathbb{Z}^n$, and $\\mathcal{E}:\\mathbb{Z}^n \\rightarrow \\operatorname{Pic}{S}$ be a map of abelian groups. We introduce the notion of a principal toric fibration $\\mathcal{X}_{\\Sigma, \\mathcal{E}}$ over the base scheme $S$, relativizing the usual toric construction for $\\Sigma$. We show that the category of ind-coherent sheaves on such a fibration is equivalent to the global section of the Kashiwara-Schapira stack twisted by a certain local system of categories with stalk $\\operatorname{Ind}\\operatorname{Coh} S$. It is a simultaneous generalization of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00832","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/2304.00832/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"}