{"paper":{"title":"Compatibility of canonical $\\ell$-adic local systems on Shimura varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Christian Klevdal, Stefan Patrikis","submitted_at":"2023-03-07T13:07:36Z","abstract_excerpt":"For a Shimura variety $(G, X)$ in the superrigid regime and neat level subgroup $K_0$, we show that the canonical family of $\\ell$-adic representations associated to a number field point $y \\in \\mathrm{Sh}_{K_0}(G, X)(F)$,\n  \\[\n  \\left\\{ \\rho_{y, \\ell} \\colon \\mathrm{Gal}(\\overline{\\mathbb{Q}}/F) \\to G^{\\mathrm{ad}}(\\mathbb{Q}_{\\ell}) \\right\\}_{\\ell},\n  \\]\n  form a compatible system of $G^{\\mathrm{ad}}(\\mathbb{Q}_{\\ell})$-representations: there is an integer $N(y)$ such that for all $\\ell$, $\\rho_{y, \\ell}$ is unramified away from $N(y) \\ell$, and for all $\\ell \\neq \\ell'$ and $v \\nmid N(y)\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03863","kind":"arxiv","version":2},"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/2303.03863/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"}