Use this URL to cite or link to this record in EThOS:
Title: Local heights and densities for curves of low genus
Author: Caselli, Marco
ISNI:       0000 0004 8497 5912
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
Availability of Full Text:
Access from EThOS:
Access from Institution:
The thesis consists of two projects, both regarding the localisations of low genus curves. In the first part we focus on the curves of genus 1. Our aim is to improve the known methods to compute the Canonical Height over an elliptic curve defined over a number field. We show how is not possible to extend directly the method of Bost and Mestre to the complex case. Then, we extend the method of Müller and Stoll for the non-archimedean local height. The second part is about non-hyperelliptic curves of genus 3. We compute close lower and upper bounds for the density of rational ternary quartics that are everywhere locally solvable by computing the density at each completion of the rationals. In the p-adic case we estimate bounds and formulas for the probabilities of solubility of all the possible reductions of a rational ternary quartic defined over Qp.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics