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There are $60$ conjugacy classes of cyclic subgroups in $W(E_7)$ and $18$ of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree $2$ can be achieved for given $q$."},"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":"1611.02832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T06:38:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a817dda3f24eb5997b3d674e1358761e519692ea34cb07618b82eea80e991aa","abstract_canon_sha256":"cf54d2741707120a9619216a6672c7b77462a1fb606274bc6a48d25780d61860"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:51.662224Z","signature_b64":"OlYFr5Q+h1Gar9rTzonm7EuIhOmTPpH8ipqN1ZEUaxg1npwBDx5Jr28E+tNDWi1VE3y27uKB+PK6lp7wWH42Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5837cd8bb8f9e3fe28177d121d5affa156857ccc50c4c775ad1ea3d4d6c5d858","last_reissued_at":"2026-05-18T00:35:51.661750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:51.661750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal del Pezzo surfaces of degree $2$ 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":"2016-11-09T06:38:31Z","abstract_excerpt":"Let $X$ be a minimal del Pezzo surface of degree $2$ over a finite field $\\mathbb{F}_q$. 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