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Arithmetic bigness and a uniform Bogomolov-type result

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 نشر من قبل Xinyi Yuan
 تاريخ النشر 2021
  مجال البحث
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 تأليف Xinyi Yuan




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In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.

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