{"paper":{"title":"On the motivic cohomology of some singular rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT","math.OA"],"primary_cat":"math.AG","authors_text":"Tess Bouis","submitted_at":"2026-08-05T11:00:25Z","abstract_excerpt":"Using non-$\\mathbb{A}^1$-invariant motivic cohomology, we prove motivic refinements of certain known computations of the algebraic $K$-theory of singular rings, such as rings of the form $\\mathbb{Z}/p^n$, $\\mathbb{Z}[x]/(x^e)$, and $\\mathscr{C}(X;\\mathbb{C})$ for $X$ a compact Hausdorff space. These refinements are made possible by the use of integral $p$-adic Hodge theory, as a replacement for the standard use of trace methods in $K$-theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05220","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/2608.05220/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"}