{"title":"完美域上平面Cremona群的代数子群","authors":"Julia Schneider, Susanna Zimmermann","doi":"10.46298/epiga.2021.6715","DOIUrl":null,"url":null,"abstract":"We show that any infinite algebraic subgroup of the plane Cremona group over\na perfect field is contained in a maximal algebraic subgroup of the plane\nCremona group. We classify the maximal groups, and their subgroups of rational\npoints, up to conjugacy by a birational map.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2020-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Algebraic subgroups of the plane Cremona group over a perfect field\",\"authors\":\"Julia Schneider, Susanna Zimmermann\",\"doi\":\"10.46298/epiga.2021.6715\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that any infinite algebraic subgroup of the plane Cremona group over\\na perfect field is contained in a maximal algebraic subgroup of the plane\\nCremona group. We classify the maximal groups, and their subgroups of rational\\npoints, up to conjugacy by a birational map.\",\"PeriodicalId\":41470,\"journal\":{\"name\":\"Epijournal de Geometrie Algebrique\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Epijournal de Geometrie Algebrique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/epiga.2021.6715\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epijournal de Geometrie Algebrique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2021.6715","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Algebraic subgroups of the plane Cremona group over a perfect field
We show that any infinite algebraic subgroup of the plane Cremona group over
a perfect field is contained in a maximal algebraic subgroup of the plane
Cremona group. We classify the maximal groups, and their subgroups of rational
points, up to conjugacy by a birational map.