Universiteit Leiden

nl en

Dissertation

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.

Author
Lido, G.M.
Date
12 October 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.

This website uses cookies.  More information.