FIRST AND SECOND <i>K</i>-GROUPS OF AN ELLIPTIC CURVE OVER A GLOBAL FIELD OF POSITIVE CHARACTERISTIC

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KONDO S., Yasuda S.

ANNALES DE L INSTITUT FOURIER, vol.68, no.5, pp.2005-2067, 2018 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 68 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.5802/aif.3202
  • Journal Name: ANNALES DE L INSTITUT FOURIER
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2005-2067
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

Abstract

In this paper, we show that the maximal divisible subgroup of groups K-1 and K-2 of an elliptic curve E over a function field is uniquely divisible. Further those K-groups modulo this uniquely divisible subgroup are explicitly computed. We also calculate the motivic cohomology groups of the minimal regular model of E, which is an elliptic surface over a finite field.