{"paper":{"title":"$ A_\\infty $-Deformations and their Derived Categories","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.KT","authors_text":"Jasper van de Kreeke","submitted_at":"2023-08-15T20:32:13Z","abstract_excerpt":"Handling curved $ A_\\infty $-deformations is challenging and defining their derived categories seems impossible. In this paper, we show how to welcome the curvature and build derived categories despite the apparent difficulties. We explicitly describe their $ A_\\infty $-structure by a deformed Kadeishvili theorem.\n  This paper starts with a review of $ A_\\infty $-deformations for non-specialists. We explain why $ A_\\infty $-deformations require curvature and why curvature supposedly causes problems. We prove that infinitesimally curved $ A_\\infty $-deformations are in fact non-problematic and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.08026","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/2308.08026/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"}