NERON SYMBOL ON ${\kappa}-HOLOMORPHIC$ TORUS

  • Sim, Kyung-Ah (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY) ;
  • Woo, Sung-Sik (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY)
  • 발행 : 2000.11.01

초록

S. Turner has shown that a Neron symbol can be calculated from the values of K-meromorphic theta functions corresponding to divisors on K-holomorphic torus of strongly diagonal type. Using an isogeny to a K-holomorphic torus of strongly diagonal type, he constructed a Neron symbol on K-holomorphic torus of diagonal type. In this work, we provide a simple formula of the Neron symbol on the Tate curve. And then we construct the Neron symbol on K-holomorphic torus of diagonal or st rongly diagonal type without using isogenies.

키워드

참고문헌

  1. Math. Ann. v.196 On nonarchimedean representations of abelian varieties L. Gerritzen
  2. Schriftereihe Math. Inst. Univ. Munster Uber ergentliche Familien algebraischer Varietaten uber affinoiden Raumen U. Kopf
  3. Fundamental of Diophantine geometry S. Lang
  4. Lecture Notes in Math v.326 Elliptic curves A. Robert
  5. Nagoya Math. J. v.69 Ultrametric theta functions and abelian varieties H. Tapia-Recillas
  6. J. Number Theory v.21 Nonarchimedean theta function and the Neron symbol S. Turner
  7. Compositio Mathematica v.107 Local height on abelian varieties with split multiplicative reduction A. Werner