On the second rational <i>K</i>-group of an elliptic curve over global fields of positive characteristic

KONDO S., Yasuda S.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, vol.102, pp.1053-1098, 2011 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102
  • Publication Date: 2011
  • Doi Number: 10.1112/plms/pdq045
  • Journal Name: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1053-1098
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

Abstract

Let E be an elliptic curve over a global field of positive characteristic. Let r be the order of zero at s = 0 of the Hasse-Weil L-function with bad factors removed. The Parshin conjecture on the vanishing of higher rational K-theory of projective smooth schemes over finite fields implies dim(Q) K-2(E) circle times(Z) Q = r. It is shown that dimQ K-2(E) circle times(Z) Q >= r.