{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AYA345NSCTP7CD2EDJHS2MLUVQ","short_pith_number":"pith:AYA345NS","schema_version":"1.0","canonical_sha256":"0601be75b214dff10f441a4f2d3174ac1285961e04e90b71dd40cbe68287c51e","source":{"kind":"arxiv","id":"1802.02322","version":2},"attestation_state":"computed","paper":{"title":"Cyclicity and indecomposability in the Brauer group of a $p$-adic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eduardo Tengan","submitted_at":"2018-02-07T06:50:31Z","abstract_excerpt":"For a $p$-adic curve $X$, we study conditions under which all classes in the $n$-torsion of $Br(X)$ are $\\mathbb{Z}/n$-cyclic. We show that in general not all classes are $\\mathbb{Z}/n$-cyclic classes. On the other hand, if $X$ has good reduction and $n$ is prime to $p$, of if $X$ is an elliptic curve over $\\mathbb{Q}_p$ with split multiplicative reduction and $n$ is a power of $p$, then we prove that all order $n$ elements of $Br(X)$ are $\\mathbb{Z}/n$-cyclic. Finally, if $X$ has good reduction and its function field $K(X)$ contains all $p^2$-th roots of $1$, we show the existence of indecomp"},"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":"1802.02322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-07T06:50:31Z","cross_cats_sorted":[],"title_canon_sha256":"38fa535487b7e78c1b32a9dd101b42fd1f6f2a098bf4184786661f1277786781","abstract_canon_sha256":"e8b9bc8435e3db260e2130321f17bb19245d7783a9c0de2bc5338c9ffe869076"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:33.680378Z","signature_b64":"r3fH3gO3Q7jokfw8RAsdCMsO/obCCFOTu6I4xiovbz2g/ctrM+AZjytUF8s+dJiahhkLcTbL5EWLXp8zWPVICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0601be75b214dff10f441a4f2d3174ac1285961e04e90b71dd40cbe68287c51e","last_reissued_at":"2026-05-17T23:49:33.679785Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:33.679785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cyclicity and indecomposability in the Brauer group of a $p$-adic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eduardo Tengan","submitted_at":"2018-02-07T06:50:31Z","abstract_excerpt":"For a $p$-adic curve $X$, we study conditions under which all classes in the $n$-torsion of $Br(X)$ are $\\mathbb{Z}/n$-cyclic. We show that in general not all classes are $\\mathbb{Z}/n$-cyclic classes. On the other hand, if $X$ has good reduction and $n$ is prime to $p$, of if $X$ is an elliptic curve over $\\mathbb{Q}_p$ with split multiplicative reduction and $n$ is a power of $p$, then we prove that all order $n$ elements of $Br(X)$ are $\\mathbb{Z}/n$-cyclic. Finally, if $X$ has good reduction and its function field $K(X)$ contains all $p^2$-th roots of $1$, we show the existence of indecomp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02322","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":"1802.02322","created_at":"2026-05-17T23:49:33.679874+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.02322v2","created_at":"2026-05-17T23:49:33.679874+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02322","created_at":"2026-05-17T23:49:33.679874+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYA345NSCTP7","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYA345NSCTP7CD2E","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYA345NS","created_at":"2026-05-18T12:32:13.499390+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/AYA345NSCTP7CD2EDJHS2MLUVQ","json":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ.json","graph_json":"https://pith.science/api/pith-number/AYA345NSCTP7CD2EDJHS2MLUVQ/graph.json","events_json":"https://pith.science/api/pith-number/AYA345NSCTP7CD2EDJHS2MLUVQ/events.json","paper":"https://pith.science/paper/AYA345NS"},"agent_actions":{"view_html":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ","download_json":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ.json","view_paper":"https://pith.science/paper/AYA345NS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.02322&json=true","fetch_graph":"https://pith.science/api/pith-number/AYA345NSCTP7CD2EDJHS2MLUVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AYA345NSCTP7CD2EDJHS2MLUVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ/action/storage_attestation","attest_author":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ/action/author_attestation","sign_citation":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ/action/citation_signature","submit_replication":"https://pith.science/pith/AYA345NSCTP7CD2EDJHS2MLUVQ/action/replication_record"}},"created_at":"2026-05-17T23:49:33.679874+00:00","updated_at":"2026-05-17T23:49:33.679874+00:00"}