{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:YRDVLO77TYB63BJUUUXELXGPBU","short_pith_number":"pith:YRDVLO77","schema_version":"1.0","canonical_sha256":"c44755bbff9e03ed8534a52e45dccf0d042d27f52746942d6b31c91b96f649fa","source":{"kind":"arxiv","id":"math/0507274","version":1},"attestation_state":"computed","paper":{"title":"Wildly ramified covers with large genus","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Rachel Pries","submitted_at":"2005-07-13T20:15:13Z","abstract_excerpt":"We study wildly ramified G-Galois covers $\\phi:Y \\to X$ branched at B (defined over an algebraically closed field of characteristic p). We show that curves Y of arbitrarily high genus occur for such covers even when G, X, B and the inertia groups are fixed. The proof relies on a Galois action on covers of germs of curves and formal patching. As a corollary, we prove that for any nontrivial quasi-p group G and for any sufficiently large integer $\\sigma$ with $p \\nmid \\sigma$, there exists a G-Galois \\'etale cover of the affine line with conductor $\\sigma$ above the point $\\infty$."},"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":"math/0507274","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-07-13T20:15:13Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f4a344fdb68404dda3cc6018ea6dd0883de87179cab789ceb9b4c297f9e9b593","abstract_canon_sha256":"ac68e09a3bf921ed9ece780410a2a19f49ef791e6dd462bf6ae515042279a550"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:52.764112Z","signature_b64":"t81L6UXNntGnifiDTXU5W5vTi7fXLfQCZID+PTE/0EVcfEGrsCLgwVQTmh9hZAyAjgrfDTEfBmNjFv/VxdzHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c44755bbff9e03ed8534a52e45dccf0d042d27f52746942d6b31c91b96f649fa","last_reissued_at":"2026-05-18T01:22:52.763461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:52.763461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wildly ramified covers with large genus","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Rachel Pries","submitted_at":"2005-07-13T20:15:13Z","abstract_excerpt":"We study wildly ramified G-Galois covers $\\phi:Y \\to X$ branched at B (defined over an algebraically closed field of characteristic p). We show that curves Y of arbitrarily high genus occur for such covers even when G, X, B and the inertia groups are fixed. The proof relies on a Galois action on covers of germs of curves and formal patching. As a corollary, we prove that for any nontrivial quasi-p group G and for any sufficiently large integer $\\sigma$ with $p \\nmid \\sigma$, there exists a G-Galois \\'etale cover of the affine line with conductor $\\sigma$ above the point $\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507274","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":"math/0507274","created_at":"2026-05-18T01:22:52.763557+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0507274v1","created_at":"2026-05-18T01:22:52.763557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507274","created_at":"2026-05-18T01:22:52.763557+00:00"},{"alias_kind":"pith_short_12","alias_value":"YRDVLO77TYB6","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"YRDVLO77TYB63BJU","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"YRDVLO77","created_at":"2026-05-18T12:25:53.939244+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/YRDVLO77TYB63BJUUUXELXGPBU","json":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU.json","graph_json":"https://pith.science/api/pith-number/YRDVLO77TYB63BJUUUXELXGPBU/graph.json","events_json":"https://pith.science/api/pith-number/YRDVLO77TYB63BJUUUXELXGPBU/events.json","paper":"https://pith.science/paper/YRDVLO77"},"agent_actions":{"view_html":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU","download_json":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU.json","view_paper":"https://pith.science/paper/YRDVLO77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0507274&json=true","fetch_graph":"https://pith.science/api/pith-number/YRDVLO77TYB63BJUUUXELXGPBU/graph.json","fetch_events":"https://pith.science/api/pith-number/YRDVLO77TYB63BJUUUXELXGPBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU/action/storage_attestation","attest_author":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU/action/author_attestation","sign_citation":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU/action/citation_signature","submit_replication":"https://pith.science/pith/YRDVLO77TYB63BJUUUXELXGPBU/action/replication_record"}},"created_at":"2026-05-18T01:22:52.763557+00:00","updated_at":"2026-05-18T01:22:52.763557+00:00"}