On the rational K2 of a curve of GL2 type over a global field of positive characteristic. Issue 2 (October 2014)

• Record Type: Journal Article
• Authors: Chida, Masataka; Kondo, Satoshi; Yamauchi, Takuya
• Is Part Of: Journal of K-Theory. Volume 14:Issue 2:Part 1(2014)
• Page Start: 313
• Page End: 342
• Publication Date: 2014-10
• Subjects: K-theory, -- function fields, -- Parshin conjecture; Primary 19F27, -- Secondary 11G40; K-theory -- Periodicals; 512.6605
• DOI: 10.1017/is014006024jkt272
• Languages: English
• ISSNs: 1865-2433

Abstract

Abstract: If is an integral model of a smooth curve X over a global field k, there is a localization sequence comparing the K -theory of and X . We show that K 1 ( ) injects into K 1 ( X ) rationally, by showing that the previous boundary map in the localization sequence is rationally a surjection, for X of "GL2 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 -elliptic sheaves of rank 2.