{"title":"正特征全局域上GL(2)型曲线的有理K(2","authors":"Masataka Chida, S. Kondo, Takuya Yamauchi","doi":"10.1017/IS014006024JKT272","DOIUrl":null,"url":null,"abstract":". If X is an integral model of a smooth curve X over a global field k , there is a localization sequence comparing the K -theory of X and X . We show that K 1 ( X ) injects into K 1 ( X ) rationally, by showing that the previous boundary map in the localization sequence is rationally a surjection, for X of “GL 2 type” and k of positive characteristic not 2. Examples are given to show that the relative G 1 term can have large rank. Examples of such curves include non-isotrivial elliptic curves, Drinfeld modular curves, and the moduli of D -elliptic sheaves of rank 2.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"114 1","pages":"313-342"},"PeriodicalIF":0.0000,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the rational K(2) of a curve of GL(2) type over a global field of positive characteristic\",\"authors\":\"Masataka Chida, S. Kondo, Takuya Yamauchi\",\"doi\":\"10.1017/IS014006024JKT272\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". If X is an integral model of a smooth curve X over a global field k , there is a localization sequence comparing the K -theory of X and X . We show that K 1 ( X ) injects into K 1 ( X ) rationally, by showing that the previous boundary map in the localization sequence is rationally a surjection, for X of “GL 2 type” and k of positive characteristic not 2. Examples are given to show that the relative G 1 term can have large rank. Examples of such curves include non-isotrivial elliptic curves, Drinfeld modular curves, and the moduli of D -elliptic sheaves of rank 2.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"114 1\",\"pages\":\"313-342\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS014006024JKT272\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS014006024JKT272","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the rational K(2) of a curve of GL(2) type over a global field of positive characteristic
. If X is an integral model of a smooth curve X over a global field k , there is a localization sequence comparing the K -theory of X and X . We show that K 1 ( X ) injects into K 1 ( X ) rationally, by showing that the previous boundary map in the localization sequence is rationally a surjection, for X of “GL 2 type” and k of positive characteristic not 2. Examples are given to show that the relative G 1 term can have large rank. Examples of such curves include non-isotrivial elliptic curves, Drinfeld modular curves, and the moduli of D -elliptic sheaves of rank 2.
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