{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:PQZHYFMXZAFFUU3LYSA5GE5ERK","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":"448e3dbb86a2c6c4e8c3908e03559c666a2583cb0f006efc7d3e1cdb9c1709f2","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2000-09-12T20:24:22Z","title_canon_sha256":"61ae7e572df07a9fb6fe0bdac754c30f2cc9aaab9ec8f5969df73371c9e27d77"},"schema_version":"1.0","source":{"id":"math/0009123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0009123","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0009123v2","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0009123","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"PQZHYFMXZAFF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"PQZHYFMXZAFFUU3L","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"PQZHYFMX","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:e431e19175aeaad3bbf0c4997e6086ad30a938fe40472e93d318ab932e4cde5d","target":"graph","created_at":"2026-05-18T01:05:38Z","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":"In his previous paper (Math. Res. Letters 7(2000), 123--132) the author proved that in characteristic zero the jacobian $J(C)$ of a hyperelliptic curve $C: y^2=f(x)$ has only trivial endomorphisms over an algebraic closure $K_a$ of the ground field $K$ if the Galois group $Gal(f)$ of the irreducible polynomial $f(x) \\in K[x]$ is either the symmetric group $S_n$ or the alternating group $A_n$. Here $n>4$ is the degree of $f$.\n In math.AG/0003002 we extended this result to the case of certain ``smaller'' Galois groups. In particular, we treated the infinite series $n=2^r+1, Gal(f)=L_2(2^r)$ and ","authors_text":"Yuri G. Zarhin","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-09-12T20:24:22Z","title":"Hyperelliptic jacobians and projective linear Galois groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009123","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":"sha256:8b9070a2bdf277927269c77e30121f33a0fb9c71cd9e7d30532f8a8f91992f37","target":"record","created_at":"2026-05-18T01:05:38Z","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":"448e3dbb86a2c6c4e8c3908e03559c666a2583cb0f006efc7d3e1cdb9c1709f2","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2000-09-12T20:24:22Z","title_canon_sha256":"61ae7e572df07a9fb6fe0bdac754c30f2cc9aaab9ec8f5969df73371c9e27d77"},"schema_version":"1.0","source":{"id":"math/0009123","kind":"arxiv","version":2}},"canonical_sha256":"7c327c1597c80a5a536bc481d313a48a88a397d4e35477a3bb5e463980f61489","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c327c1597c80a5a536bc481d313a48a88a397d4e35477a3bb5e463980f61489","first_computed_at":"2026-05-18T01:05:38.301158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:38.301158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwgxN9BOi9Qjmbj1vqIC2ZJRX14hJp7pO1TGIScLv3pBG0oosUT2Rjq3LhXVHa4eA8KA/g9i0QaTek9nlFvwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:38.301698Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0009123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b9070a2bdf277927269c77e30121f33a0fb9c71cd9e7d30532f8a8f91992f37","sha256:e431e19175aeaad3bbf0c4997e6086ad30a938fe40472e93d318ab932e4cde5d"],"state_sha256":"d1386784b9ac5ce32a9572e184da593d81d2cb713104145c8ed946cb1cc020c8"}