{"paper":{"title":"Affine representability results in ${\\mathbb A}^1$-homotopy theory I: vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Aravind Asok, Marc Hoyois, Matthias Wendt","submitted_at":"2015-06-23T17:02:36Z","abstract_excerpt":"We establish a general \"affine representability\" result in ${\\mathbb A}^1$-homotopy theory over a general base. We apply this result to obtain representability results for vector bundles in ${\\mathbb A}^1$-homotopy theory. Our results simplify and significantly generalize F. Morel's ${\\mathbb A}^1$-representability theorem for vector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07093","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"}