{"paper":{"title":"Motivic model categories and motivic derived algebraic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Yuki Kato","submitted_at":"2017-03-08T14:31:27Z","abstract_excerpt":"In this paper, we develop an enhancement of derived algebraic geometry to apply to $\\mathbb{A}^1$-homotopy theory introduced by Morel and Voevodsky. We call the enhancement \"motivic derived algebraic geometry\". We shall actually formulate \"motivic\" versions of $\\infty$-categories, $\\infty$-topoi, spectral schemes and spectral Deligne--Mumford stacks established by Joyal, Lurie, To\\\"en and Vezzosi.\n  By using the language of motivic derived algebraic geometry, we construct the Grassmannian and the algebraic $K$-theory. Furthermore we formulate the Thom spaces for vector bundles on (motivic) sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02849","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":""},"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"}