{"paper":{"title":"TR with logarithmic poles and the de Rham-Witt complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Faidon Andriopoulos","submitted_at":"2024-12-01T18:35:47Z","abstract_excerpt":"In the article of Hesselholt [Hes05], a set of conjectures is laid out. Given a smooth scheme $X$ over the ring of integers $\\mathcal{O}_K$ of a $p$-adic field $K$, these conjectures concern the expected relation between log topological restriction homology $\\mathrm{TR}^r (X,M_X)$ and the absolute log de Rham--Witt complex $W_r\\Omega_{(X,M_X)}$.\n  In this note, which is companion to [And24a], we discuss the case of a $p$-completely smooth $p$-adic formal scheme $X$ over $\\mathrm{spf} \\mathcal{O}_C$, where $C$ is the field of $p$-adic complex numbers.\n  Along the way, we study the motivic filtr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00929","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.00929/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"}