{"paper":{"title":"Rank 2 $\\ell$-adic local systems and Higgs bundles over a curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Hongjie Yu","submitted_at":"2023-01-30T18:35:20Z","abstract_excerpt":"Let $X$ be a smooth, projective, and geometrically connected curve defined over a finite field $\\mathbb{F}_q$ of characteristic $p$ different from $2$ and $S\\subseteq X$ a subset of closed points. Let $\\overline{X}$ and $\\overline{S}$ be their base changes to an algebraic closure of $\\mathbb{F}_q$. We study the number of $\\ell$-adic local systems $(\\ell\\neq p)$ in rank $2$ over $\\overline{X}-\\overline{S}$ with all possible prescribed tame local monodromies fixed by $k$-fold iterated action of Frobenius endomorphism for every $k\\geq 1$. In all cases, we confirm conjectures of Deligne predicting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13157","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/2301.13157/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"}