Canonical heights on elliptic curves in characteristic p

abstract

• Let k = double-struck F signq(t) be the rational function field with finite constant field and characteristic p 3, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curve E/K which has ordinary reduction at all places of K extending v, we consider a canonical height pairing , v: E(Ksep) x E(Ksep) xv which is symmetric, bilinear and Galois equivariant. The pairing , for the "infinite" place of k is a natural extension of the classical Nron-Tate height. For v finite, the pairing , .v plays the role of global analytic p-adic heights. We further determine some hypotheses for the nondegeneracy of these pairings.

authors

• Papanikolas, Matthew

published proceedings

• COMPOSITIO MATHEMATICA

author list (cited authors)

• Papanikolas, M. A.

citation count

• 2

complete list of authors

• Papanikolas, MA

publication date

• July 2000

publisher

• Cambridge University Press (CUP)  Publisher

published in

• Compositio Mathematica  Journal

keywords

• Elliptic Curves
• Global Canonical Heights
• Global Function Fields
• Mazur-tate Sigma Function

Digital Object Identifier (DOI)

• 10.1023/A:1002054316957

start page

• 299

end page

• 313

volume

• 122

issue

• 3

URL

• http://dx.doi.org/10.1023/a:1002054316957