{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AYA345NSCTP7CD2EDJHS2MLUVQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e8b9bc8435e3db260e2130321f17bb19245d7783a9c0de2bc5338c9ffe869076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-07T06:50:31Z","title_canon_sha256":"38fa535487b7e78c1b32a9dd101b42fd1f6f2a098bf4184786661f1277786781"},"schema_version":"1.0","source":{"id":"1802.02322","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02322","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02322v2","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02322","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"AYA345NSCTP7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AYA345NSCTP7CD2E","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AYA345NS","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:fdc5565d2358268080ea654841f9dea0bd59cb29815a476b23936f00d58caf1d","target":"graph","created_at":"2026-05-17T23:49:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Eduardo Tengan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-07T06:50:31Z","title":"Cyclicity and indecomposability in the Brauer group of a $p$-adic curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02322","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ec29c51de7296bade643274d3d4189d8a83f083eadab0117ed83598dd2cc4f1d","target":"record","created_at":"2026-05-17T23:49:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e8b9bc8435e3db260e2130321f17bb19245d7783a9c0de2bc5338c9ffe869076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-07T06:50:31Z","title_canon_sha256":"38fa535487b7e78c1b32a9dd101b42fd1f6f2a098bf4184786661f1277786781"},"schema_version":"1.0","source":{"id":"1802.02322","kind":"arxiv","version":2}},"canonical_sha256":"0601be75b214dff10f441a4f2d3174ac1285961e04e90b71dd40cbe68287c51e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0601be75b214dff10f441a4f2d3174ac1285961e04e90b71dd40cbe68287c51e","first_computed_at":"2026-05-17T23:49:33.679785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:33.679785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r3fH3gO3Q7jokfw8RAsdCMsO/obCCFOTu6I4xiovbz2g/ctrM+AZjytUF8s+dJiahhkLcTbL5EWLXp8zWPVICQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:33.680378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02322","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec29c51de7296bade643274d3d4189d8a83f083eadab0117ed83598dd2cc4f1d","sha256:fdc5565d2358268080ea654841f9dea0bd59cb29815a476b23936f00d58caf1d"],"state_sha256":"8aca0f215c02088e9bd033ac12c754812b9a6bd3439e80ccc05ea3d06a9535f6"}