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Let $K$ be an imaginary quadratic field satisfying a modified \"Heegner hypothesis\" in which $p$ splits, write $K_\\infty$ for the anticyclotomic $\\mathbb Z_p$-extension of $K$ and let $\\Lambda$ denote the Iwasawa algebra of $K_\\infty/K$. By extending to the supersingular case the $\\Lambda$-adic Kolyvagin method originally developed by Bertolini in the ordinary setting, we prove that Kobayashi's plus/minus $p$-primary Selmer groups of $E$ over $K_\\infty$ have corank $1$ over $\\Lambd"},"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":"1503.07812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-26T18:22:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"711dea62d1e4a0e8701eb9e5e30df074a5d67b46b8685730b7c32849436716cf","abstract_canon_sha256":"8ebec6bee1e36595ad778227e92d60be89f445e1936d8c38e03e023ca65d0ea1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:18.698560Z","signature_b64":"/9110EfiXJZ5V9W07YduaUR2KLFmiwOjb8KnJ0WCTwnABuII86ITR8zvEVAOGOkuDPvkfCQWERujbVbU79AmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c375b0c9557dc253e8ef03ff90524413c8523eb04a1a4b99efa040b80917d5aa","last_reissued_at":"2026-05-18T02:20:18.698020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:18.698020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Matteo Longo, Stefano Vigni","submitted_at":"2015-03-26T18:22:55Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb Q$ and let $p\\geq5$ be a prime of good supersingular reduction for $E$. 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By extending to the supersingular case the $\\Lambda$-adic Kolyvagin method originally developed by Bertolini in the ordinary setting, we prove that Kobayashi's plus/minus $p$-primary Selmer groups of $E$ over $K_\\infty$ have corank $1$ over $\\Lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07812","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":"1503.07812","created_at":"2026-05-18T02:20:18.698109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.07812v1","created_at":"2026-05-18T02:20:18.698109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07812","created_at":"2026-05-18T02:20:18.698109+00:00"},{"alias_kind":"pith_short_12","alias_value":"YN23BSKVPXBF","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YN23BSKVPXBFH2HP","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YN23BSKV","created_at":"2026-05-18T12:29:50.041715+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/YN23BSKVPXBFH2HPAP7ZAUSECP","json":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP.json","graph_json":"https://pith.science/api/pith-number/YN23BSKVPXBFH2HPAP7ZAUSECP/graph.json","events_json":"https://pith.science/api/pith-number/YN23BSKVPXBFH2HPAP7ZAUSECP/events.json","paper":"https://pith.science/paper/YN23BSKV"},"agent_actions":{"view_html":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP","download_json":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP.json","view_paper":"https://pith.science/paper/YN23BSKV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.07812&json=true","fetch_graph":"https://pith.science/api/pith-number/YN23BSKVPXBFH2HPAP7ZAUSECP/graph.json","fetch_events":"https://pith.science/api/pith-number/YN23BSKVPXBFH2HPAP7ZAUSECP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP/action/storage_attestation","attest_author":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP/action/author_attestation","sign_citation":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP/action/citation_signature","submit_replication":"https://pith.science/pith/YN23BSKVPXBFH2HPAP7ZAUSECP/action/replication_record"}},"created_at":"2026-05-18T02:20:18.698109+00:00","updated_at":"2026-05-18T02:20:18.698109+00:00"}