RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars





You may need the following programs to see the files








Globus Seminar
April 25, 2013 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)
 


On the size of generators of solutions of some Diophantine equations

M. Hindryab

a Université Paris VII – Denis Diderot
b Laboratoire J.-V. Poncelet, Independent University of Moscow
Video records:
Flash Video 252.4 Mb
Flash Video 476.8 Mb

Number of views:
This page:71
Video files:8


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: It has been known since at least Fermat that the set of integral solutions to the equation x^2-dy^2=1 form a finitely generated group of rank one. It has been known since at least Poincaré that the set of rational solutions to equations of the type y^2=x^3+ax+b form a group; in fact, as Mordell proved, the latter group is also finitely generated.
There is a natural notion of size or height of solutions, so an important and natural question is to estimate the minimal size of a set of generators. The questions can easily be generalized on one hand to the group of units of a number field and, on the other hand, to the group of rational points of an abelian variety over a global field.
The answer for the first case is essentially known, though there are important unsettled related questions; the answer for the second case is essentially conjectural. We will discuss what we know, conjecture and give examples where theorems may be proven. This will take us to a journey through some arithmetic geometry, zeta functions etc., i.e. several number theorists favourite toys.

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017