Mathematische Annalen

, Volume 340, Issue 1, pp 223–235

The l-component of the unipotent Albanese map

Article

DOI: 10.1007/s00208-007-0151-x

Cite this article as:
Kim, M. & Tamagawa, A. Math. Ann. (2008) 340: 223. doi:10.1007/s00208-007-0151-x

Abstract

We prove a finiteness theorem for the local l ≠  p-component of the \({\mathbb{Q}}_p\) -unipotent Albanese map for curves. As an application, we refine the non-abelian Selmer varieties arising in the study of global points and deduce thereby a new proof of Siegel’s theorem for affine curves over \({\mathbb{Q}}\) of genus one with Mordell–Weil rank at most one.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Korea Institute of Advanced StudySeoulSouth Korea
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan