An introduction to height theory
The notion of height was invented by André Weil to prove the famous Mordell's conjecture (if A is an abelian variety defined over a number field K, then A(K) is a finitely generated abelian group). In this class, we will study some properties of the logarithmic, absolute Weil height. We will also discuss about open problems related to this useful tool. At the end, we will construct an analogue of this height on elliptic curves.
Lecturer
Date
13th October, 2023 ~ 12th January, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Friday | 13:30 - 16:55 | A3-1-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Algebraic number theory, Galois theory, local fields
Reference
1. E. Bombieri and W. Gubler, Heights in Diophantine geometry. Cambridge University Press, Cambridge, 2006.
2. D. Masser, Auxiliary polynomials in number theory. Cambridge University press, Cambridge, 2016.
3. J. Silverman, Advanced topics in the arithmetic of Elliptic curves, Springer-Verlag, GTM 151, 1995.
2. D. Masser, Auxiliary polynomials in number theory. Cambridge University press, Cambridge, 2016.
3. J. Silverman, Advanced topics in the arithmetic of Elliptic curves, Springer-Verlag, GTM 151, 1995.
Audience
Graduate
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Arnaud Plessis is an assistant professor at BIMSA from September 2023. His research is mainly focused on diophantine geometry. He obtained his Phd. thesis in 2019 at Université de Caen Normandie. Before joining BIMSA, he has been Attaché Temporaire d'Enseignement et de Recherche (a kind of postdoctoral with course duties) at Université Grenoble Alpes from September 2019 to August 2020. Then, he has been postdoctor at Morningside Center of Mathematics, Chinese Academy of Sciences, from September 2020 to August 2023.