{"paper":{"title":"Nilpotent invariant motives I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.KT"],"primary_cat":"math.AG","authors_text":"Satoshi Mochizuki","submitted_at":"2017-02-20T15:31:15Z","abstract_excerpt":"The purpose of this article is to clarify the question what makes motives $\\mathbb{A}^1$-homotopy invariance. we give construction of the stable model category of nilpotent invariant motives $\\mathcal{M}ot_{\\operatorname{dg}}^{\\operatorname{nilp}}$ and define the nilpotent invriant motives associated with schemes and relative exact categories. For a noetherian scheme $X$, there are two kind of motives associated with $X$ in the homotopy category $\\operatorname{Ho}(\\mathcal{M}ot^{\\operatorname{nilp}}_{\\operatorname{dg}})$, namely $M_{\\operatorname{nilp}}(X)$ and $M_{\\operatorname{nilp}}'(X)$. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06013","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":""},"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"}