{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:26KG5MLSZYJ5GE3JRIMM7XI6RT","short_pith_number":"pith:26KG5MLS","schema_version":"1.0","canonical_sha256":"d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c","source":{"kind":"arxiv","id":"2410.23453","version":2},"attestation_state":"computed","paper":{"title":"Ramification bounds via Wach modules and q-crystalline cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Pavel \\v{C}oupek","submitted_at":"2024-10-30T20:51:01Z","abstract_excerpt":"Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance of $q$-crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of $\\mathrm{H}^{i}_{et}(X_{\\mathbb{C}_K}, \\mathbb{Z}/p\\mathbb{Z})$ for a smooth proper $p$-adic formal scheme $X$ over $\\mathcal{O}_K$, for arbitrarily large degree $i$."},"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":"2410.23453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-10-30T20:51:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d3ab14de735f6ef548a4bd4a2c9e499fec2c119cb2b969e2a577cb221389cc85","abstract_canon_sha256":"a74ecb14a99592bd6a16183afb7a747b88d5e949d6852db8c2eba685134e2be1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:25.627123Z","signature_b64":"eUnS5jOyMj7fFsqVn9gP4xNq0Y2qngw3VCHkgOt+IpFzIussHDKk+/frZguevyFxYhhmP9FcOyJU87a/a2EWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c","last_reissued_at":"2026-05-28T01:04:25.626547Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:25.626547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramification bounds via Wach modules and q-crystalline cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Pavel \\v{C}oupek","submitted_at":"2024-10-30T20:51:01Z","abstract_excerpt":"Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance of $q$-crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of $\\mathrm{H}^{i}_{et}(X_{\\mathbb{C}_K}, \\mathbb{Z}/p\\mathbb{Z})$ for a smooth proper $p$-adic formal scheme $X$ over $\\mathcal{O}_K$, for arbitrarily large degree $i$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23453","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.23453/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2410.23453","created_at":"2026-05-28T01:04:25.626606+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.23453v2","created_at":"2026-05-28T01:04:25.626606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23453","created_at":"2026-05-28T01:04:25.626606+00:00"},{"alias_kind":"pith_short_12","alias_value":"26KG5MLSZYJ5","created_at":"2026-05-28T01:04:25.626606+00:00"},{"alias_kind":"pith_short_16","alias_value":"26KG5MLSZYJ5GE3J","created_at":"2026-05-28T01:04:25.626606+00:00"},{"alias_kind":"pith_short_8","alias_value":"26KG5MLS","created_at":"2026-05-28T01:04:25.626606+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/26KG5MLSZYJ5GE3JRIMM7XI6RT","json":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT.json","graph_json":"https://pith.science/api/pith-number/26KG5MLSZYJ5GE3JRIMM7XI6RT/graph.json","events_json":"https://pith.science/api/pith-number/26KG5MLSZYJ5GE3JRIMM7XI6RT/events.json","paper":"https://pith.science/paper/26KG5MLS"},"agent_actions":{"view_html":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT","download_json":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT.json","view_paper":"https://pith.science/paper/26KG5MLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.23453&json=true","fetch_graph":"https://pith.science/api/pith-number/26KG5MLSZYJ5GE3JRIMM7XI6RT/graph.json","fetch_events":"https://pith.science/api/pith-number/26KG5MLSZYJ5GE3JRIMM7XI6RT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT/action/storage_attestation","attest_author":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT/action/author_attestation","sign_citation":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT/action/citation_signature","submit_replication":"https://pith.science/pith/26KG5MLSZYJ5GE3JRIMM7XI6RT/action/replication_record"}},"created_at":"2026-05-28T01:04:25.626606+00:00","updated_at":"2026-05-28T01:04:25.626606+00:00"}