{"paper":{"title":"Une conjecture $C_{\\rm st}$ pour la cohomologie \\`a support compact","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Pierre Colmez, Sally Gilles, Wies{\\l}awa Nizio{\\l}","submitted_at":"2025-11-18T17:17:13Z","abstract_excerpt":"Let $\\mathbf{B}$ be the ring of analytic functions on the Fargues-Fontaine curve $Y_{\\rm FF}$. We show that adding $p$-adic analogs of $\\log p$ and $\\log 2\\pi i$ kills its Galois cohomology in degrees~$\\geq 1$. The analogous result for $\\mathbf{B}^+_{\\rm dR}$ is folklore. This makes it possible to formulate $C_{\\rm dR}$ and $C_{\\rm st}$-type conjectures for compact support cohomology of $p$-adic analytic varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.14675","kind":"arxiv","version":3},"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/2511.14675/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"}