{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AYBXBC3W7DY43AVIFNFNQ2P57F","short_pith_number":"pith:AYBXBC3W","schema_version":"1.0","canonical_sha256":"0603708b76f8f1cd82a82b4ad869fdf96388da7b8df972065f0e4821481d5ef5","source":{"kind":"arxiv","id":"1701.01890","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.01890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-07T22:10:08Z","cross_cats_sorted":[],"title_canon_sha256":"7f9089c40c8dddce2555c2b3656fa9ea8fd49aa5d0824056964b118f2e88a1b0","abstract_canon_sha256":"f286bc47b3f0fb11875a317c9e303c264c02ffdcd7176e4cdfa93d8244cf483d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:13.186067Z","signature_b64":"KjfqYnvdx1G1cNAVIFWxT6IB7HRXTd1Zv5wNV3Pjh2WdL9uvujnwIK8h1pGKrGSYPhisfC01fqnoAsygNfsTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0603708b76f8f1cd82a82b4ad869fdf96388da7b8df972065f0e4821481d5ef5","last_reissued_at":"2026-05-18T00:53:13.185470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:13.185470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.01890","created_at":"2026-05-18T00:53:13.185596+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.01890v1","created_at":"2026-05-18T00:53:13.185596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01890","created_at":"2026-05-18T00:53:13.185596+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYBXBC3W7DY4","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYBXBC3W7DY43AVI","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYBXBC3W","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F","json":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F.json","graph_json":"https://pith.science/api/pith-number/AYBXBC3W7DY43AVIFNFNQ2P57F/graph.json","events_json":"https://pith.science/api/pith-number/AYBXBC3W7DY43AVIFNFNQ2P57F/events.json","paper":"https://pith.science/paper/AYBXBC3W"},"agent_actions":{"view_html":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F","download_json":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F.json","view_paper":"https://pith.science/paper/AYBXBC3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.01890&json=true","fetch_graph":"https://pith.science/api/pith-number/AYBXBC3W7DY43AVIFNFNQ2P57F/graph.json","fetch_events":"https://pith.science/api/pith-number/AYBXBC3W7DY43AVIFNFNQ2P57F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F/action/storage_attestation","attest_author":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F/action/author_attestation","sign_citation":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F/action/citation_signature","submit_replication":"https://pith.science/pith/AYBXBC3W7DY43AVIFNFNQ2P57F/action/replication_record"}},"created_at":"2026-05-18T00:53:13.185596+00:00","updated_at":"2026-05-18T00:53:13.185596+00:00"}