{"paper":{"title":"Deformations of local systems and Eisenstein series","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"A. Braverman, D. Gaitsgory","submitted_at":"2006-05-04T19:05:08Z","abstract_excerpt":"Let $X$ be a (smooth and complete) curve and $G$ a reductive group. In [BG] we introduced the object that we called \"geometric Eisenstein series\". This is a perverse sheaf $\\bar{Eis}_E$ (or rather a complex of such) on the moduli stack $Bun_G(X)$ of principal $G$-bundles on $X$, which is attached to a local system $E$ on $X$ with respect to the torus $\\check{T}$, Langlands dual to the Cartan subgroup $T\\subset G$. In loc. cit. we showed that$\\bar{Eis}_E$ corresponds to the $\\check{G}$-local system induced from $E$, in the sense of the geometric Langlands correspondence.\n  In the present paper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605139","kind":"arxiv","version":4},"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/0605139/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"}