{"paper":{"title":"TR and the $r$-Nygaard filtered prismatic cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.AG","authors_text":"Faidon Andriopoulos","submitted_at":"2024-12-01T18:04:24Z","abstract_excerpt":"Given an animated ring $S$, we define a filtration on its absolute prismatic cohomology $\\mathcal{N}_r^{\\geq i} \\mathbb{\\Delta}_S$, which we call the $r$-Nygaard filtration and study some of its main properties using a mixture of algebraic and homotopy theoretic techniques. This filtration is obtained by suitably gluing $r$-copies of the usual Nygaard filtration and corresponds to the $\\xi_r$-adic filtration on $\\mathbb{A}_{\\mathrm{inf}}$, in the case that $S$ is a perfectoid ring.\n  Using this, we study the motivic filtration of topological restriction homology $\\mathrm{TR}^r (S;\\mathbb{Z}_p)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00914","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/2412.00914/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"}