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In this paper we define a filtration $F^{r}$ of the group $CH_{0}(A)$ and prove an isomorphism $\\frac{K(k;A,...,A)}{\\Sym}\\otimes\\mathbb{Z}[\\frac{1}{r!}]\\simeq F^{r}/F^{r+1}\\otimes\\mathbb{Z}[\\frac{1}{r!}]$, where $K(k;A,...,A)$ is the Somekawa K-group attached to $r$-copies of the abelian variety $A$.\\\\ In the special case when $k$ is a finite extension of $\\mathbb{Q}_{p}$ and $A$ has split multiplicative reduction, we compute the kernel of the map $CH_{0}(A)\\otimes\\Z[\\frac{1}{2}]\\rightarrow \\rm{Hom}(Br(A),\\Q/\\Z)\\otimes\\Z[\\frac{1}{2}]$, in"},"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":"1305.6284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-27T18:16:34Z","cross_cats_sorted":[],"title_canon_sha256":"a9d6c7b60a255ecb5d62d50f8ab81078085ccab6c7663518207b1d11ce6b6e2d","abstract_canon_sha256":"5c444421753a492f5c9f88fd27c70ca2d98964a8130466337a5975b5a41adf26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.477676Z","signature_b64":"9bic+mT2rIiKfOJW+XuWx8HSPSLwCf77YqjpVwPPnhPYvnjd4cT2HYiahSPpDiPuyYWf+nH/MKPEyG09cApXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a65530037d74fd0b5c27fefa929b814f4c5901aeb6c8f6ef8a0f56662ac9db","last_reissued_at":"2026-05-17T23:53:17.477008Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.477008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Filtration of CH_{0} for an Abelian Variety A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Evangelia Gazaki","submitted_at":"2013-05-27T18:16:34Z","abstract_excerpt":"Let $A$ be an abelian variety defined over a field $k$. In this paper we define a filtration $F^{r}$ of the group $CH_{0}(A)$ and prove an isomorphism $\\frac{K(k;A,...,A)}{\\Sym}\\otimes\\mathbb{Z}[\\frac{1}{r!}]\\simeq F^{r}/F^{r+1}\\otimes\\mathbb{Z}[\\frac{1}{r!}]$, where $K(k;A,...,A)$ is the Somekawa K-group attached to $r$-copies of the abelian variety $A$.\\\\ In the special case when $k$ is a finite extension of $\\mathbb{Q}_{p}$ and $A$ has split multiplicative reduction, we compute the kernel of the map $CH_{0}(A)\\otimes\\Z[\\frac{1}{2}]\\rightarrow \\rm{Hom}(Br(A),\\Q/\\Z)\\otimes\\Z[\\frac{1}{2}]$, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6284","kind":"arxiv","version":2},"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":"1305.6284","created_at":"2026-05-17T23:53:17.477102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6284v2","created_at":"2026-05-17T23:53:17.477102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6284","created_at":"2026-05-17T23:53:17.477102+00:00"},{"alias_kind":"pith_short_12","alias_value":"3CTFKMADPV2P","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3CTFKMADPV2P2C24","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3CTFKMAD","created_at":"2026-05-18T12:27:32.513160+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/3CTFKMADPV2P2C24E77PVEU3QF","json":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF.json","graph_json":"https://pith.science/api/pith-number/3CTFKMADPV2P2C24E77PVEU3QF/graph.json","events_json":"https://pith.science/api/pith-number/3CTFKMADPV2P2C24E77PVEU3QF/events.json","paper":"https://pith.science/paper/3CTFKMAD"},"agent_actions":{"view_html":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF","download_json":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF.json","view_paper":"https://pith.science/paper/3CTFKMAD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6284&json=true","fetch_graph":"https://pith.science/api/pith-number/3CTFKMADPV2P2C24E77PVEU3QF/graph.json","fetch_events":"https://pith.science/api/pith-number/3CTFKMADPV2P2C24E77PVEU3QF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF/action/storage_attestation","attest_author":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF/action/author_attestation","sign_citation":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF/action/citation_signature","submit_replication":"https://pith.science/pith/3CTFKMADPV2P2C24E77PVEU3QF/action/replication_record"}},"created_at":"2026-05-17T23:53:17.477102+00:00","updated_at":"2026-05-17T23:53:17.477102+00:00"}