Highly Influenced

# 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} }

- 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).

#### From This Paper

##### Topics from this paper.

1 Citations

5 References

Similar Papers

#### Citations

##### Publications citing this paper.

#### References

##### Publications referenced by this paper.

Showing 1-5 of 5 references