{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JZOFOONDYQDJB6PS2JEAFSDN2S","short_pith_number":"pith:JZOFOOND","schema_version":"1.0","canonical_sha256":"4e5c5739a3c40690f9f2d24802c86dd48b1c8a9b893c77518864906082ac9119","source":{"kind":"arxiv","id":"1106.0513","version":1},"attestation_state":"computed","paper":{"title":"The Stickelberger splitting map and Euler systems in the $K$--theory of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.NT","authors_text":"Cristian D. Popescu, Grzegorz Banaszak","submitted_at":"2011-06-02T21:08:05Z","abstract_excerpt":"For a CM abelian extension $F/K$ of an arbitrary totally real number field $K$, we construct the Stickelberger splitting maps (in the sense of \\cite{Ba1}) for both the \\'etale and the Quillen $K$--theory of $F$ and we use these maps to construct Euler systems in the even Quillen $K$--theory of $F$. The Stickelberger splitting maps give an immediate proof of the annihilation of the groups of divisible elements $div K_{2n}(F)_l$ of the even $K$--theory of the top field by higher Stickelberger elements, for all odd primes $l$. This generalizes the results of \\cite{Ba1}, which only deals with CM a"},"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":"1106.0513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-02T21:08:05Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"0f732773996496a80b19d8365a6b65b7cca0eabcc81b6355e62acbb223775fe3","abstract_canon_sha256":"c2659dd15d185d3621d1e5f71226e5b8d2862e9c436600fe793c7d12b1570c99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:49.282874Z","signature_b64":"fGXhQqhPaF/0N/HhR9DU3akHwqiPemApaX+cx2txE6aqPtlxj71jA4M7ZPg8jvoZU7Wp7PAPHOzMBYY5TIRpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e5c5739a3c40690f9f2d24802c86dd48b1c8a9b893c77518864906082ac9119","last_reissued_at":"2026-05-18T04:20:49.277674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:49.277674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Stickelberger splitting map and Euler systems in the $K$--theory of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.NT","authors_text":"Cristian D. Popescu, Grzegorz Banaszak","submitted_at":"2011-06-02T21:08:05Z","abstract_excerpt":"For a CM abelian extension $F/K$ of an arbitrary totally real number field $K$, we construct the Stickelberger splitting maps (in the sense of \\cite{Ba1}) for both the \\'etale and the Quillen $K$--theory of $F$ and we use these maps to construct Euler systems in the even Quillen $K$--theory of $F$. The Stickelberger splitting maps give an immediate proof of the annihilation of the groups of divisible elements $div K_{2n}(F)_l$ of the even $K$--theory of the top field by higher Stickelberger elements, for all odd primes $l$. This generalizes the results of \\cite{Ba1}, which only deals with CM a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0513","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":"1106.0513","created_at":"2026-05-18T04:20:49.281414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0513v1","created_at":"2026-05-18T04:20:49.281414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0513","created_at":"2026-05-18T04:20:49.281414+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZOFOONDYQDJ","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZOFOONDYQDJB6PS","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZOFOOND","created_at":"2026-05-18T12:26:32.869790+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/JZOFOONDYQDJB6PS2JEAFSDN2S","json":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S.json","graph_json":"https://pith.science/api/pith-number/JZOFOONDYQDJB6PS2JEAFSDN2S/graph.json","events_json":"https://pith.science/api/pith-number/JZOFOONDYQDJB6PS2JEAFSDN2S/events.json","paper":"https://pith.science/paper/JZOFOOND"},"agent_actions":{"view_html":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S","download_json":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S.json","view_paper":"https://pith.science/paper/JZOFOOND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0513&json=true","fetch_graph":"https://pith.science/api/pith-number/JZOFOONDYQDJB6PS2JEAFSDN2S/graph.json","fetch_events":"https://pith.science/api/pith-number/JZOFOONDYQDJB6PS2JEAFSDN2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S/action/storage_attestation","attest_author":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S/action/author_attestation","sign_citation":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S/action/citation_signature","submit_replication":"https://pith.science/pith/JZOFOONDYQDJB6PS2JEAFSDN2S/action/replication_record"}},"created_at":"2026-05-18T04:20:49.281414+00:00","updated_at":"2026-05-18T04:20:49.281414+00:00"}