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

Published online by Cambridge University Press:  28 July 2014

Masataka Chida ,
Satoshi Kondo  and
Takuya Yamauchi
Masataka Chida
Affiliation:
Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japanchida@math.kyoto-u.ac.jp
Satoshi Kondo
Affiliation:
Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japansatoshi.kondo@ipmu.jp
Takuya Yamauchi
Affiliation:
Department of mathematics, Faculty of Education, Kagoshima University, Korimoto 1-20-6 Kagoshima 890-0065, Japan Department of mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canadayamauchi@edu.kagoshima-u.ac.jp, tyama@math.toronto.edu
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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 K1 () 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 -elliptic sheaves of rank 2.

Keywords

K-theoryfunction fieldsParshin conjecturePrimary 19F27Secondary 11G40

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Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 2 , October 2014 , pp. 313 - 342
Copyright
Copyright © ISOPP 2014 

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