{"paper":{"title":"Finiteness for \\'{E}tale Fundamental Groups of N\\'{e}ron Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frank Lu","submitted_at":"2026-06-30T22:19:19Z","abstract_excerpt":"In this paper, we prove that the \\'{e}tale fundamental group of the N\\'{e}ron model of an abelian variety over a number field $K$ is the semidirect product of a finite group with the \\'{e}tale fundamental group of the ring of integers of $K.$ We prove this by studying how the Faltings height of an abelian variety changes under covers that spread out to finite \\'{e}tale covers of its N\\'{e}ron model. We then strengthen this result for elliptic curves. Using Merel's torsion theorem, we show the size of this finite group can be uniformly bounded for a fixed number field. We conclude by giving the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00232","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/2607.00232/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"}