Bivariate polynomial injections and elliptic curves

Hector Pasten ^[1]
1. [1] Pontificia Universidad Católica de Chile
  
  Pontificia Universidad Católica de Chile
  
  Santiago, Chile
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-0548-x
Enlaces
- Texto completo
Resumen
- For every number field k, we construct an affine algebraic surface X over k with a Zariski dense set of k-rational points, and a regular function f on X inducing an injective map X(k)→k on k-rational points. In fact, given any elliptic curve E of positive rank over k, we can take X=V×V with V a suitable affine open set of E. The method of proof combines value distribution theory for complex holomorphic maps with results of Faltings on rational points in sub-varieties of abelian varieties.