{"paper":{"title":"Motives with modulus, III: The categories of motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Bruno Kahn, Hiroyasu Miyazaki, Shuji Saito, Takao Yamazaki","submitted_at":"2020-11-22T07:54:46Z","abstract_excerpt":"We construct and study a triangulated category of motives with modulus $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ over a field $k$ that extends Voevodsky's category $\\mathbf{DM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ in such a way as to encompass non-homotopy invariant phenomena. In a similar way as $\\mathbf{DM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ is constructed out of smooth $k$-varieties, $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ is constructed out of proper modulus pairs, introduced in Part I of this work. To such a modulus pair we associate its motive in $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.11859","kind":"arxiv","version":3},"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/2011.11859/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"}