A Remark on the Rank of Jacobians of Hyperelliptic Curves over Q over Certain Elementary Abelian 2-extensions

@inproceedings{2EXTENSIONS1988ARO,
  title={A Remark on the Rank of Jacobians of Hyperelliptic Curves over Q over Certain Elementary Abelian 2-extensions},
  author={ABELIAN 2-EXTENSIONS},
  year={1988}
}
  • ABELIAN 2-EXTENSIONS
  • Published 1988
1. Introduction. A nice question in arithmetic geometry is whether for a given abelian variety A over a number field K, relatively small extensions LZDK exist such that rank(A(L)) is "much" bigger than rank(A(UL)). Already in 1938, Billing (see [5; p. 157] for a reference) showed that the elliptic curve E/Q given by the equation y 2 = x* — x has rank at least m over infinitely many fields of the form Q(l/dΓ, , VΊQ). 

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