{"paper":{"title":"Abelian surfaces good away from 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Akio Tamagawa, Christopher Rasmussen","submitted_at":"2015-04-13T02:14:10Z","abstract_excerpt":"Fix a number field $k$ and a rational prime $\\ell$. We consider abelian varieties whose $\\ell$-power torsion generates a pro-$\\ell$ extension of $k(\\mu_{\\ell^\\infty})$ which is unramified away from $\\ell$. It is a necessary, but not generally sufficient, condition that such varieties have good reduction away from $\\ell$. In the special case of $\\ell = 2$, we demonstrate that for abelian surfaces $A/\\mathbb{Q}$, good reduction away from $\\ell$ does suffice. The result is extended to elliptic curves and abelian surfaces over certain number fields unramified away from $\\{2,\\infty\\}$. An explicit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03047","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"}