On the Kernel of the Reciprocity Map of Normal Surfaces over Finite Fields*

  • Matsumi, Kazuya
  • Sato, Kanetomo
  • Asakura, Masanori

  • 1Mathematical Institute, Tohoku University, Aramaki-aza-Aoba, Aoba-ku, Sendai 980, Japan

    2Department of Mathematics, Tokyo Institute of Technology, 12-1 Oh-okayama 2-chome, Meguro-ku, Tokyo 152, Japan

    3Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606, Japan

K-Theory 18(3):p 203-234, November 1999.

The reciprocity map of a smooth proper variety over a finite field is known to have a trivial kernel and dense image. In this paper, we investigate the reciprocity map of a normal surface proper over a finite field and give two examples of normal projective surfaces whose reciprocity maps are not injective.

Copyright ©1999 Kluwer Academic Publishers