{"paper":{"title":"On the semisimplicity of reductions and adelic openness for $E$-rational compatible systems over global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gebhard B\\\"ockle, Sebastian Petersen, Wojciech Gajda","submitted_at":"2019-01-11T17:09:12Z","abstract_excerpt":"Let $X$ be a normal geometrically connected variety over a finite field $\\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups of arbitrary connected $E$-rational semisimple compatible systems $(\\rho_\\lambda)$ of $n$-dimensional representations of the arithmetic fundamental group $\\pi_1(X)$, where $\\lambda$ ranges over the finite places of $E$ not above $p$: Let $\\Lambda_\\lambda$ be any $\\pi_1(X)$-stable lattice in $E_\\lambda^n$ under $\\rho_\\lambda$. Then for almost all $\\lambda$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03654","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":""},"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"}