Commun. Korean Math. Soc. 2000 Vol. 15, No. 1, 37-44
Kyung Ah Shim, Sung Sik Woo Ewha Womans University, Ewha Womans University
Abstract : In this paper, for a given $p$-adic quasicharacter $c_v:k_v^* \rightarrow \Bbb Q_p$ satisfying a special condition, we will explicitly construct an admissible pairing corresponding to $c_v$. We define a $p$-adic height on the arbitrary abelian varieties associated to divisors and $c_v$ by using admissible pairings at every nonarchimedean places. We also show that our $p$-adic height satisfies similar properties of N\'eron-Tate's canonical $p$-adic height.