On the rational K2 of a curve of GL2 type over a global field of positive characteristic

Masataka Chida, Satoshi Kondo, Takuya Yamauchi

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Abstract

If script 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 script X and X. We show that K1(script X) injects into K1 (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 G1 term can have large rank. Examples of such curves include non-isotrivial elliptic curves, Drinfeld modular curves, and the moduli of script D-elliptic sheaves of rank 2.

Original languageEnglish
Pages (from-to)313-342
Number of pages30
JournalJournal of K-Theory
Volume7
Issue number1
DOIs
Publication statusPublished - 2014 Jun 30

Keywords

  • K-theory
  • Parshin conjecture
  • function fields

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