{"paper":{"title":"The Motivic Cofiber of $\\tau$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bogdan Gheorghe","submitted_at":"2017-01-17T21:37:43Z","abstract_excerpt":"Consider the Tate twist $\\tau \\in H^{0,1}(S^{0,0})$ in the mod 2 cohomology of the motivic sphere. After 2-completion, the motivic Adams spectral sequence realizes this element as a map $\\tau \\colon S^{0,-1} \\to S^{0,0}$, with cofiber $C\\tau$. We show that this motivic 2-cell complex can be endowed with a unique $E_{\\infty}$ ring structure. Moreover, this promotes the known isomorphism $\\pi_{\\ast,\\ast} C\\tau \\cong \\mathrm{Ext}^{\\ast,\\ast}_{BP_{\\ast}BP}(BP_{\\ast},BP_{\\ast})$ to an isomorphism of rings which also preserves higher products.\n  We then consider the closed symmetric monoidal categor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04877","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"}