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The image $\\Gamma$ of the Galois group $\\operatorname{Gal}(\\overline{\\mathbb{F}}_q / \\mathbb{F}_q)$ in the group $\\operatorname{Aut}(\\mathrm{Pic}(\\overline{X}))$ is a cyclic subgroup preserving the anticanonical class and the intersection form. The conjugacy class of $\\Gamma$ in the subgroup of $\\operatorname{Aut}(\\mathrm{Pic}(\\overline{X}))$ preserving the anticanonical class and the intersection form is a natural invariant of $X$. We say that the conjugacy class of $\\Gamma$ in $\\operatorname{Aut}(\\mat"},"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":"1803.07421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-17T23:43:13Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c686ad5ef4893bc74e26f686b96281b30477eaa964772b9353f0cce94740258f","abstract_canon_sha256":"70148e28209b4b1fa245a6cffd8caded238a35ae7ec3d859e6bcdf96738a29c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:33.279640Z","signature_b64":"c6aei4DXjfrTneOZ/5sdt6frCJcuJzrht8+I53w531UW7Tx/o8H+hgUjiY5Y00HuczQS1y/XE+M5rjNyiqrFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"266ded952b7cd3ab342e460b78739e591d99c9402a2f6f3afda77960d544fb74","last_reissued_at":"2026-05-18T00:20:33.279061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:33.279061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Del Pezzo surfaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Andrey Trepalin","submitted_at":"2018-03-17T23:43:13Z","abstract_excerpt":"Let $X$ be a del Pezzo surface of degree $2$ or greater over a finite field $\\mathbb{F}_q$. The image $\\Gamma$ of the Galois group $\\operatorname{Gal}(\\overline{\\mathbb{F}}_q / \\mathbb{F}_q)$ in the group $\\operatorname{Aut}(\\mathrm{Pic}(\\overline{X}))$ is a cyclic subgroup preserving the anticanonical class and the intersection form. The conjugacy class of $\\Gamma$ in the subgroup of $\\operatorname{Aut}(\\mathrm{Pic}(\\overline{X}))$ preserving the anticanonical class and the intersection form is a natural invariant of $X$. We say that the conjugacy class of $\\Gamma$ in $\\operatorname{Aut}(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07421","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":"1803.07421","created_at":"2026-05-18T00:20:33.279150+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07421v1","created_at":"2026-05-18T00:20:33.279150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07421","created_at":"2026-05-18T00:20:33.279150+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZW63FJLPTJ2","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZW63FJLPTJ2WNBO","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZW63FJL","created_at":"2026-05-18T12:32:22.470017+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/EZW63FJLPTJ2WNBOIYFXQ446LE","json":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE.json","graph_json":"https://pith.science/api/pith-number/EZW63FJLPTJ2WNBOIYFXQ446LE/graph.json","events_json":"https://pith.science/api/pith-number/EZW63FJLPTJ2WNBOIYFXQ446LE/events.json","paper":"https://pith.science/paper/EZW63FJL"},"agent_actions":{"view_html":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE","download_json":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE.json","view_paper":"https://pith.science/paper/EZW63FJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07421&json=true","fetch_graph":"https://pith.science/api/pith-number/EZW63FJLPTJ2WNBOIYFXQ446LE/graph.json","fetch_events":"https://pith.science/api/pith-number/EZW63FJLPTJ2WNBOIYFXQ446LE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE/action/storage_attestation","attest_author":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE/action/author_attestation","sign_citation":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE/action/citation_signature","submit_replication":"https://pith.science/pith/EZW63FJLPTJ2WNBOIYFXQ446LE/action/replication_record"}},"created_at":"2026-05-18T00:20:33.279150+00:00","updated_at":"2026-05-18T00:20:33.279150+00:00"}