{"paper":{"title":"Chiral de Rham complex","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arkady Vaintrob, Fyodor Malikov, Vadim Schechtman","submitted_at":"1998-03-11T13:37:33Z","abstract_excerpt":"The aim of this note is to define certain sheaves of vertex algebras on smooth manifolds. For each smooth complex algebraic (or analytic) manifold $X$, we construct a sheaf $\\Omega^{ch}_X$, called the {\\bf chiral de Rham complex} of $X$. It is a sheaf of vertex algebras in the Zarisky (or classical) topology, It comes equipped with a $\\BZ$-grading by {\\it fermionic charge}, and the {\\it chiral de Rham differential} $d_{DR}^{ch}$, which is an endomorphism of degree 1 such that $(d_{DR}^{ch})^2=0$. One has a canonical embedding of the usual de Rham complex $(\\Omega_X, d_{DR})\\hra (\\Omega_X^{ch},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803041","kind":"arxiv","version":7},"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/math/9803041/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"}