{"paper":{"title":"Equivariant algebraic $\\mathrm{K}$-theory and Artin $L$-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.AT","math.NT"],"primary_cat":"math.KT","authors_text":"Elden Elmanto, Ningchuan Zhang","submitted_at":"2024-05-06T15:52:17Z","abstract_excerpt":"In this paper, we generalize the Quillen-Lichtenbaum Conjecture relating special values of Dedekind zeta functions to algebraic $\\mathrm{K}$-groups. The former has been settled by Rost-Voevodsky up to the Iwasawa Main Conjecture. Our generalization extends the scope of this conjecture to Artin $L$-functions of Galois representations of finite, function, and totally real number fields. The statement of this conjecture relates norms of the special values of these $L$-functions to sizes of equivariant algebraic $\\mathrm{K}$-groups with coefficients in an equivariant Moore spectrum attached to a G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03578","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/2405.03578/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"}