{"paper":{"title":"The Picard group of motivic A(1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bogdan Gheorghe, Daniel C. Isaksen, Nicolas Ricka","submitted_at":"2016-06-16T14:05:20Z","abstract_excerpt":"We show that the Picard group $Pic(A(1))$ of the stable category of modules over $\\mathbb{C}$-motivic $A(1)$ is isomorphic to $\\mathbb{Z}^4$. By comparison, the Picard group of classical $A(1)$ is $\\mathbb{Z}^2 \\oplus \\mathbb{Z}/2$. One extra copy of $\\mathbb{Z}$ arises from the motivic bigrading. The joker is a well-known exotic element of order $2$ in the Picard group of classical $A(1)$. The $\\mathbb{C}$-motivic joker has infinite order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05191","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"}