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- W3003139682 abstract "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 Muller 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." @default.
- W3003139682 created "2020-01-30" @default.
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- W3003139682 date "2018-09-01" @default.
- W3003139682 modified "2023-09-23" @default.
- W3003139682 title "Local heights and densities for curves of low genus" @default.
- W3003139682 hasPublicationYear "2018" @default.
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