{"paper":{"title":"A special case of the two-dimensional Jacobian Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vered Moskowicz","submitted_at":"2016-05-31T19:59:59Z","abstract_excerpt":"Let $f: \\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ be a $\\mathbb{C}$-algebra endomorphism having an invertible Jacobian. We show that for such $f$, if, in addition, the group of invertible elements of $\\mathbb{C}[f(x),f(y),x][1/v] \\subset \\mathbb{C}(x,y)$ is contained in $\\mathbb{C}(f(x),f(y))-0$, then $f$ is an automorphism. Here $v \\in \\mathbb{C}[f(x),f(y)]-0$ is such that $y = u/v$, with $u \\in \\mathbb{C}[f(x),f(y),x]-0$. Keller's theorem (in dimension two) follows immediately, since Keller's condition $\\mathbb{C}(f(x),f(y))=\\mathbb{C}(x,y)$ implies that the group of invertible elements of $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00426","kind":"arxiv","version":2},"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"}