{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AJKSZKPHOLDEFGQXZVNE3GLUGE","short_pith_number":"pith:AJKSZKPH","schema_version":"1.0","canonical_sha256":"02552ca9e772c6429a17cd5a4d9974313c6a3a9e34a6ac7f7e62f7ba9bfd77ad","source":{"kind":"arxiv","id":"1710.09043","version":1},"attestation_state":"computed","paper":{"title":"Construction of Anti-Cyclotomic Euler Systems of Abelian Varieties Associated to $X_1(N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Heon Kim, Daeyeol Jeon. Byoung Du Kim","submitted_at":"2017-10-25T01:51:38Z","abstract_excerpt":"Let $K$ be an imaginary quadratic field, $N$ be a positive integer, $f(z)$ be a newform of level $\\Gamma_1(N)$, and $A_f$ be the abelian variety associated to $f$. For each $\\tau \\in K$ ($\\operatorname{Im} \\tau >0$), we construct a certain point $P_\\tau$ on $A_f$ defined over an extended ring class field of $K$ of level $N$. Our construction generalizes Birch's construction of the Heegner points to the abelian varieties associated to modular forms of level $\\Gamma_1(N)$ and nontrivial character. Then, we show that $P_\\tau$'s satisfy the distribution and congruence relations of an Euler system,"},"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":"1710.09043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-25T01:51:38Z","cross_cats_sorted":[],"title_canon_sha256":"ebe2afc4aaf324db13e75de66ee42862b307a59c7250c5e2614cbd1b5813b7b8","abstract_canon_sha256":"2580ae006744998a5251be5fc4b68ea8ec2a1656f3fbca3a852bf2db760c695e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:00.494345Z","signature_b64":"sgCKcmZ7uCwCigJlNawO7ddxQYgCowHjmnr1bpWAdzPLVMchY/wY828tROqgddLK7h7QvOoNv0Tyx/K+ZdvVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02552ca9e772c6429a17cd5a4d9974313c6a3a9e34a6ac7f7e62f7ba9bfd77ad","last_reissued_at":"2026-05-18T00:32:00.493930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:00.493930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of Anti-Cyclotomic Euler Systems of Abelian Varieties Associated to $X_1(N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Heon Kim, Daeyeol Jeon. Byoung Du Kim","submitted_at":"2017-10-25T01:51:38Z","abstract_excerpt":"Let $K$ be an imaginary quadratic field, $N$ be a positive integer, $f(z)$ be a newform of level $\\Gamma_1(N)$, and $A_f$ be the abelian variety associated to $f$. For each $\\tau \\in K$ ($\\operatorname{Im} \\tau >0$), we construct a certain point $P_\\tau$ on $A_f$ defined over an extended ring class field of $K$ of level $N$. Our construction generalizes Birch's construction of the Heegner points to the abelian varieties associated to modular forms of level $\\Gamma_1(N)$ and nontrivial character. Then, we show that $P_\\tau$'s satisfy the distribution and congruence relations of an Euler system,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09043","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":"1710.09043","created_at":"2026-05-18T00:32:00.493995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09043v1","created_at":"2026-05-18T00:32:00.493995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09043","created_at":"2026-05-18T00:32:00.493995+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJKSZKPHOLDE","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJKSZKPHOLDEFGQX","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJKSZKPH","created_at":"2026-05-18T12:31:05.417338+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/AJKSZKPHOLDEFGQXZVNE3GLUGE","json":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE.json","graph_json":"https://pith.science/api/pith-number/AJKSZKPHOLDEFGQXZVNE3GLUGE/graph.json","events_json":"https://pith.science/api/pith-number/AJKSZKPHOLDEFGQXZVNE3GLUGE/events.json","paper":"https://pith.science/paper/AJKSZKPH"},"agent_actions":{"view_html":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE","download_json":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE.json","view_paper":"https://pith.science/paper/AJKSZKPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09043&json=true","fetch_graph":"https://pith.science/api/pith-number/AJKSZKPHOLDEFGQXZVNE3GLUGE/graph.json","fetch_events":"https://pith.science/api/pith-number/AJKSZKPHOLDEFGQXZVNE3GLUGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE/action/storage_attestation","attest_author":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE/action/author_attestation","sign_citation":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE/action/citation_signature","submit_replication":"https://pith.science/pith/AJKSZKPHOLDEFGQXZVNE3GLUGE/action/replication_record"}},"created_at":"2026-05-18T00:32:00.493995+00:00","updated_at":"2026-05-18T00:32:00.493995+00:00"}