{"paper":{"title":"Strongly compatible systems associated to semistable abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Mark Kisin, Rong Zhou","submitted_at":"2025-05-04T15:57:27Z","abstract_excerpt":"We prove a motivic refinement of a result of Weil, Deligne and Raynaud on the existence of strongly compatible systems associated to abelian varieties. More precisely, given\n  an abelian variety $A$ over a number field $\\mathrm{E}\\subset \\mathbb C$, we prove that after replacing $\\mathbb E$ by a finite extension, the action of $\\mathrm{Gal}(\\overline{\\mathrm E}/\\mathrm E)$ on the $\\ell$-adic cohomology $\\mathrm H^1_{\\mathrm{\\acute{e}t}}(A_{\\overline{\\mathrm E}},\\mathbb Q_\\ell)$ gives rise to a strongly compatible system of $\\ell$-adic representations valued in the Mumford--Tate group $\\mathbf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02165","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/2505.02165/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"}