## 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 K_{1}(script 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 script D-elliptic sheaves of rank 2.

Original language | English |
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Pages (from-to) | 313-342 |

Number of pages | 30 |

Journal | Journal of K-Theory |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 Jun 30 |

## Keywords

- K-theory
- Parshin conjecture
- function fields

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