{"title":"There are no Keller maps having prime degree field extensions","authors":"Vered Moskowicz","doi":"arxiv-2407.13795","DOIUrl":null,"url":null,"abstract":"The two-dimensional Jacobian Conjecture says that a Keller map $f: (x,y)\n\\mapsto (p,q) \\in k[x,y]^2$ having an invertible Jacobian is an automorphism of\n$k[x,y]$. We prove that there is no Keller map with $[k(x,y): k(p,q)]$ prime.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.13795","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The two-dimensional Jacobian Conjecture says that a Keller map $f: (x,y)
\mapsto (p,q) \in k[x,y]^2$ having an invertible Jacobian is an automorphism of
$k[x,y]$. We prove that there is no Keller map with $[k(x,y): k(p,q)]$ prime.
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