VARIATION OF THE CANONICAL HEIGHT ON ELLIPTIC-SURFACES .3. GLOBAL BOUNDEDNESS PROPERTIES

[摘要] Let E --> C be an elliptic surface defined over a number field K, let P:C --> E be a section, and for each t is-an-element-of C(K), let h(P(t)) be the canonical height of P(t) is-an-element-of E(t) (KBAR). Tate has used a global argument to show that, up to a bounded quantity, the function t bar arrow pointing right h(P(t)) is equal to a Weil height function h(C)(t) on C. In this paper we precisely describe the behavior of the difference h(P(t)) - h(C)(t) as a function of t. (C) 1994 Academic Press, Inc.

[发布日期] 1994-09-01