{"paper":{"title":"Motives with modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.AG","authors_text":"Bruno Kahn, Shuji Saito, Takao Yamazaki","submitted_at":"2015-11-23T07:44:21Z","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 \\emph{proper modulus pairs}, that is, pairs of a proper $k$-variety $X$ and an effective divisor $D$ on $X$ such that $X \\setminus |D|$ is smooth. To a mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07124","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}