{"title":"不存在具有素度域扩展的凯勒映射","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":"{\"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}","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}
There are no Keller maps having prime degree field extensions
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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