{"paper":{"title":"On filtered algebraic $K$-theory of stacks I: characteristic zero","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Dmitry Kubrak, Elden Elmanto, Vladimir Sosnilo","submitted_at":"2025-03-13T01:00:16Z","abstract_excerpt":"Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of $X$. We prove an analog of this result for algebraic $K$-theory over a field of characteristic 0. In our setting $G$ is a reductive group that acts on a derived algebraic space $X$ with the assumption that all stabilizer groups are nice (in the sense of Alper). Our main result identifies the value $R^{\\mathrm{dAff}}K([X/G])$ of right Kan extension of the $K$-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.09928","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/2503.09928/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"}