{"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}
引用次数: 1
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.
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