Article

Mathematische Annalen

, Volume 340, Issue 1, pp 223-235

The l-component of the unipotent Albanese map

  • Minhyong KimAffiliated withDepartment of Mathematics, Purdue UniversityKorea Institute of Advanced Study Email author 
  • , Akio TamagawaAffiliated withResearch Institute for Mathematical Sciences, Kyoto University

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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.