{"paper":{"title":"Desuspensions of S^1 /\\ P^1_Q-{0,1,infty}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Kirsten Wickelgren","submitted_at":"2015-02-27T03:23:51Z","abstract_excerpt":"We use the Galois action on $\\pi_1^{\\textrm{et}}(\\mathbb{P}_{\\overline{\\mathbb{Q}}}^1 - \\{0,1,\\infty \\})$ to show that the homotopy equivalence $S^1 \\wedge (\\mathbb{G}_{m,\\mathbb{Q}} \\vee \\mathbb{G}_{m,\\mathbb{Q}}) \\cong S^1 \\wedge (\\mathbb{P}_{\\mathbb{Q}}^1 - \\{0,1,\\infty \\}) $ coming from purity does not desuspend to a map $\\mathbb{G}_{m,\\mathbb{Q}} \\vee \\mathbb{G}_{m,\\mathbb{Q}} \\to \\mathbb{P}_{\\mathbb{Q}}^1 - \\{0,1,\\infty \\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07811","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"}