Proefschrift
Geometric quadratic Chabauty and other topics in number theory
This thesis is is made of three parts. The first part describes a generalization of the Chabauty's method, that can be used to determine the rational points of a curve such that s+g>r+1, where g is the genusof the curve, r is the rank of the Mordell-Weil group of the jacobian of the curve and s is the rank of the Neron-severi of the jacobian of the curve.
- Auteur
- Lido, G.M.
- Datum
- 12 oktober 2021
- Links
- Thesis in Leiden Repository
This thesis is is made of three parts.
The first part describes a generalization of the Chabauty's method, that can be used to determine the rational points of a curve such that s+g>r+1, where g is the genusof the curve, r is the rank of the Mordell-Weil group of the jacobian of the curve and s is the rank of the Neron-severi of the jacobian of the curve.
The second part proves that for all but a finite number of Cartan modular curves, the automorphisms are only the "expected" ones.
The last part describes an algorithm that solves in quasi-polynomial time the discrete logarithm problem in all finite fields whose characteristic is "small" with respect to the cardinality.