The aim of this thesis is to provide an introduction to the study of elliptic curves
and modular forms over general commutative rings or schemes. We will recall a few
aspects of the classical theory of these objects (over the complex numbers) while
placing emphasis on the geometric picture. Moreover, we will formulate the theory
of elliptic curves in the modern language of algebraic geometry following the work of
Katz and Mazur. In addition, we provide an application of p−adic modular
forms to the theory of p−adic heights on elliptic curves.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/42925 |
| Date | 16 November 2021 |
| Creators | Besrour, Khalil |
| Contributors | Sebbar, Abdellah |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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