{"paper":{"title":"Categorical cyclic homology and filtered $\\mathcal{D}$-modules on stacks: Koszul duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AG","authors_text":"Harrison Chen","submitted_at":"2023-01-17T15:18:42Z","abstract_excerpt":"Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered $\\mathcal{D}$-modules on a smooth stack $X$ and the category of $S^1$-equivariant ind-coherent sheaves on its formal loop space $\\widehat{\\mathcal{L}} X$, exchanging compact $\\mathcal{D}$-modules with coherent sheaves, and coherent $\\mathcal{D}$-modules with continuous ind-coherent sheaves. The equivalence yields a sheaf of categories over $\\mathbb{A}^1/\\mathbb{G}_m$ whose special fiber is a category of coherent sheaves on stacks appearing in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.06949","kind":"arxiv","version":3},"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/2301.06949/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"}