{"paper":{"title":"On the relative dual of an $S^1$-gerbe over an orbifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.KT"],"primary_cat":"math.AG","authors_text":"Hsian-Hua Tseng, Ilya Shapiro, Xiang Tang","submitted_at":"2013-12-27T19:04:45Z","abstract_excerpt":"We construct a new effective orbifold $\\widehat{\\Y}$ with an $S^1$-gerbe $c$ to study an $S^1$-gerbe $\\mathfrak{t}$ on a $G$-gerbe $\\Y$ over an orbifold $\\B$. We view the former as the relative dual, relative to $\\B$, of the latter. We show that the two pairs $(\\Y, \\mathfrak{t})$ and $(\\widehat{\\Y}, c)$ have isomorphic categories of sheaves, and also the associated twisted groupoid algebras are Morita equivalent. As a corollary, the K-theory and cohomology groups of $(\\Y, \\mathfrak{t})$ and $(\\widehat{\\Y}, c)$ are isomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7316","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"}