On the rational <i>K</i><sub>2</sub> of a curve of GL<sub>2</sub> type over a global field of positive characteristic

Chida M., KONDO S., Yamauchi T.

JOURNAL OF K-THEORY, vol.14, no.2, pp.313-342, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.1017/is014006024jkt272
  • Journal Name: JOURNAL OF K-THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.313-342
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

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.