{"paper":{"title":"Stability of Elliptic Fargues-Scholze $L$-packets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.RT","authors_text":"Chenji Fu","submitted_at":"2024-12-31T21:24:38Z","abstract_excerpt":"Let $F$ be a non-archimedean local field. Let $\\overline{F}$ be an algebraic closure of $F$. Let $G$ be a connected reductive group over $F$. Let $\\varphi$ be an elliptic $L$-parameter. For every irreducible representation $\\pi$ of $G(F)$ with Fargues--Scholze $L$-parameter $\\varphi$, we prove that there exists a finite set of irreducible representations $\\{\\pi_i\\}_{i \\in I}$ containing $\\pi$, such that $\\pi_i$ has Fargues--Scholze $L$-parameter $\\varphi$ for all $i \\in I$ and a certain non-zero $\\mathbb{Z}$-linear combination $\\Theta_{\\pi_0}$ of the Harish-Chandra characters of $\\{\\pi_i\\}_{i "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00652","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/2501.00652/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"}