{"paper":{"title":"A $p$-adic Simpson correspondence for singular rigid-analytic varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The category of pro-étale vector bundles on a proper rigid-analytic variety is equivalent to the category of Higgs bundles on its eh-site.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hanlin Cai, Zeyu Liu","submitted_at":"2025-12-24T20:45:05Z","abstract_excerpt":"Let $C$ be a complete, algebraically closed non-archimedean extension of $\\mathbb{Q}_p$, and $X$ be a proper rigid-analytic variety over $C$. We show that the category of pro-\\'etale vector bundles on $X$ is equivalent to the category of Higgs bundles on the $\\eh$-site of $X$, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the category of pro-étale vector bundles on X is equivalent to the category of Higgs bundles on the eh-site of X.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"X is a proper rigid-analytic variety over a complete algebraically closed non-archimedean extension C of Q_p, with the eh-site suitably defined to handle singular cases.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The category of pro-étale vector bundles on a proper rigid-analytic variety X over C is equivalent to the category of Higgs bundles on the eh-site of X.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The category of pro-étale vector bundles on a proper rigid-analytic variety is equivalent to the category of Higgs bundles on its eh-site.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3cffa111dbafa10206bc78ec04c8ef36c0452d3e5753d9b20b04f751fc96abfc"},"source":{"id":"2512.21418","kind":"arxiv","version":2},"verdict":{"id":"0bf4baab-c0ec-44b8-9cd6-5264c063d2a8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:17:00.192110Z","strongest_claim":"We show that the category of pro-étale vector bundles on X is equivalent to the category of Higgs bundles on the eh-site of X.","one_line_summary":"The category of pro-étale vector bundles on a proper rigid-analytic variety X over C is equivalent to the category of Higgs bundles on the eh-site of X.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"X is a proper rigid-analytic variety over a complete algebraically closed non-archimedean extension C of Q_p, with the eh-site suitably defined to handle singular cases.","pith_extraction_headline":"The category of pro-étale vector bundles on a proper rigid-analytic variety is equivalent to the category of Higgs bundles on its eh-site."},"references":{"count":49,"sample":[{"doi":"","year":1984,"title":"261, Springer Berlin, 1984","work_id":"2341b229-f7f0-48a9-8d12-63eeb2b24c7f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Bhargav Bhatt and David Hansen, The six functors for zariski-constructible sheaves in rigid geometry, Compositio Mathematica 158 (2022), no. 2, 437--482","work_id":"560daeee-c775-4c4d-950a-ba01d5811811","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Bhargav Bhatt, Aspects of p-adic Hodge theory , https://www.math.ias.edu/ bhatt/teaching/mat517f25/pHT-notes.pdf","work_id":"d02a2bc8-6034-43b1-9da2-89e2d3f455e7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"flattening techniques, Mathematische Annalen 296 (1993), 403--429","work_id":"d1963f4b-6906-40ca-8635-13e45c191613","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Integral p-adic Hodge theory","work_id":"4097e7f5-464a-4d97-b1a9-626a6094626b","ref_index":5,"cited_arxiv_id":"1602.03148","is_internal_anchor":true}],"resolved_work":49,"snapshot_sha256":"867879432a5b3af9fbad0315a49eddc17c97a36c990d2399a301be4c3f2ee921","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"28cea1cccfebbb70fb125f08b0fd7a2820ca49d905186bbc2568575bb56fcab6"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}