Bertini and Northcott

Abstract

We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian varieties over a number field K to the case of jacobian varieties defined over a suitable extension of K.

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Correspondence to Fabien Pazuki.

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Pazuki, F., Widmer, M. Bertini and Northcott. Res. number theory 7, 12 (2021). https://doi.org/10.1007/s40993-021-00236-2

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Keywords

  • Bertini
  • Northcott
  • Height
  • Abelian varieties

Mathematics Subject Classification

  • 11G10
  • 11G30
  • 11G50
  • 14G40
  • 14K15