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The l-component of the unipotent Albanese map

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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.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA

    Minhyong Kim

  2. Korea Institute of Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, South Korea

    Minhyong Kim

  3. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Akio Tamagawa

Authors
  1. Minhyong Kim
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  2. Akio Tamagawa
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Correspondence to Minhyong Kim.

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Kim, M., Tamagawa, A. The l-component of the unipotent Albanese map. Math. Ann. 340, 223–235 (2008). https://doi.org/10.1007/s00208-007-0151-x

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  • DOI: https://doi.org/10.1007/s00208-007-0151-x

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