{"paper":{"title":"Large 2-adic Galois image and non-existence of certain abelian surfaces over Q","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Armand Brumer, Kenneth Kramer","submitted_at":"2017-01-07T22:10:08Z","abstract_excerpt":"Motivated by our arithmetic applications, we required some tools that might be of independent interest.\n  Let $\\mathcal E$ be an absolutely irreducible group scheme of rank $p^4$ over $\\mathbb Z_p$. We provide a complete description of the Honda systems of $p$-divisible groups $\\mathcal G$ such that $\\mathcal G[p^{n+1}]/\\mathcal G[p^n] \\simeq \\mathcal E$ for all $n$. Then we find a bound for the abelian conductor of the second layer $\\mathbb Q_p(\\mathcal G[p^2])/\\mathbb Q_p(\\mathcal G[p])$, stronger in our case than can be deduced from Fontaine's bound.\n  Let $\\pi\\!: \\, {\\rm Sp}_{2g}(\\mathbb Z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01890","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"}