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Our main result is that if the Gross-Jaulent conjecture holds for $(F,p)$ then there is a natural isomorphism $D_F^{[i,n]}\\cong\\mathcal{E}_F/p^n$ where $\\math"},"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":"1709.06465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T14:42:29Z","cross_cats_sorted":[],"title_canon_sha256":"cf9a3b9af6b6b80a62435f304c85dc6d2484f073994953aa660c94fba7b28a9b","abstract_canon_sha256":"df048288cd6634d0617307b4b155b23611d2eef147c8745b8f9e9fdbf0559a9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:45.738869Z","signature_b64":"Oc1S7aq7YxVs3a0arxM5eNbQqG3qz9/FICgcB91doeMCJPC6ULd3Ngcr21H2Pzg+CQ1BBmmldIgx9Co8AHZSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d876931b034894ab3482319df9fdac10762d6767c39d9c16c28ca4889f77643","last_reissued_at":"2026-05-18T00:34:45.738062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:45.738062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tate kernels, etale K-theory and the Gross kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Hutchinson","submitted_at":"2017-09-19T14:42:29Z","abstract_excerpt":"For an odd prime $p$ and a number field $F$ containing a $p$th root of unity, we study generalised Tate kernels, $D_F^{[i,n]}$, for $i\\in \\mathbb{Z}$ and $n\\geq 1$, having the properties that if $i\\geq 2$ and if either $p$ does not divide $i$ or $\\mu_{p^n}\\subset F$ then there are natural isomorphisms $D_F^{[i,n]}\\cong K^{\\mbox{\\tiny \\'et}}_{2i-1}(O_F^S)/p^n$, and that they are periodic modulo a power of $p$ which depends on $F$ and $n$. Our main result is that if the Gross-Jaulent conjecture holds for $(F,p)$ then there is a natural isomorphism $D_F^{[i,n]}\\cong\\mathcal{E}_F/p^n$ where $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06465","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":"1709.06465","created_at":"2026-05-18T00:34:45.738214+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.06465v1","created_at":"2026-05-18T00:34:45.738214+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06465","created_at":"2026-05-18T00:34:45.738214+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWDWSMNQGSEU","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWDWSMNQGSEUVM2I","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWDWSMNQ","created_at":"2026-05-18T12:31:12.930513+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/DWDWSMNQGSEUVM2IEMM57H62YE","json":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE.json","graph_json":"https://pith.science/api/pith-number/DWDWSMNQGSEUVM2IEMM57H62YE/graph.json","events_json":"https://pith.science/api/pith-number/DWDWSMNQGSEUVM2IEMM57H62YE/events.json","paper":"https://pith.science/paper/DWDWSMNQ"},"agent_actions":{"view_html":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE","download_json":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE.json","view_paper":"https://pith.science/paper/DWDWSMNQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.06465&json=true","fetch_graph":"https://pith.science/api/pith-number/DWDWSMNQGSEUVM2IEMM57H62YE/graph.json","fetch_events":"https://pith.science/api/pith-number/DWDWSMNQGSEUVM2IEMM57H62YE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE/action/storage_attestation","attest_author":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE/action/author_attestation","sign_citation":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE/action/citation_signature","submit_replication":"https://pith.science/pith/DWDWSMNQGSEUVM2IEMM57H62YE/action/replication_record"}},"created_at":"2026-05-18T00:34:45.738214+00:00","updated_at":"2026-05-18T00:34:45.738214+00:00"}