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Course by D. V. Osipov "Elliptic curves and their arithmetic properties"
September 7–December 7, 2020, Steklov Mathematical Institute, Room. 213 (8 Gubkina)

An elliptic curve over a field is a smooth projective curve of genus 1 which has a point defined over the basic field. In other words, a genus 1 curve is a curve which has a rational differential form without poles and zeros, or, equivalently, it is a smooth cubic curve in the two-dimensional projective space. On the set of points of elliptic curve which are defined over the basic field one can introduce the structure of an abelian group. If the ground field is the field of complex numbers, then this group is not very interesting, because it is isomorphic to a two-dimensional torus. If the ground field is finite, then one obtains a finite group which has a lot of applications in coding theory. If the ground field is the field of rational numbers, then one can prove that the resulting abelian group is finitely generated. A lot of famous conjectures in arithmetic algebraic geometry are connected with invariants of this group. It is supposed that participants of the course know the basics of Galois theory, the theory of p-adic numbers, and the theory of algebraic curves.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Program

RSS: Forthcoming seminars

Lecturer
Osipov Denis Vasilievich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by D. V. Osipov "Elliptic curves and their arithmetic properties", September 7–December 7, 2020

December 7, 2020 (Mon)
1. Lecture 14. Elliptic curves and their arithmetic properties
D. V. Osipov
December 7, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

November 30, 2020 (Mon)
2. Lecture 13. Elliptic curves and their arithmetic properties
D. V. Osipov
November 30, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

November 23, 2020 (Mon)
3. Lecture 12. Elliptic curves and their arithmetic properties
D. V. Osipov
November 23, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

November 16, 2020 (Mon)
4. Lecture 11. Elliptic curves and their arithmetic properties
D. V. Osipov
November 16, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

November 9, 2020 (Mon)
5. Lecture 10. Elliptic curves and their arithmetic properties
D. V. Osipov
November 9, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

November 2, 2020 (Mon)
6. Lecture 9. Elliptic curves and their arithmetic properties
D. V. Osipov
November 2, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

October 26, 2020 (Mon)
7. Lecture 8. Elliptic curves and their arithmetic properties
D. V. Osipov
October 26, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

October 19, 2020 (Mon)
8. Lecture 7. Elliptic curves and their arithmetic properties
D. V. Osipov
October 19, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

October 12, 2020 (Mon)
9. Lecture 6. Elliptic curves and their arithmetic properties
D. V. Osipov
October 12, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

October 5, 2020 (Mon)
10. Lecture 5. Elliptic curves and their arithmetic properties
D. V. Osipov
October 5, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

September 28, 2020 (Mon)
11. Lecture 4. Elliptic curves and their arithmetic properties
D. V. Osipov
September 28, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

September 21, 2020 (Mon)
12. Lecture 3. Elliptic curves and their arithmetic properties
D. V. Osipov
September 21, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

September 14, 2020 (Mon)
13. Лекция 2. Эллиптические кривые и их арифметические свойства
D. V. Osipov
September 14, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  

September 7, 2020 (Mon)
14. Lecture 1. Elliptic curves and their arithmetic properties
D. V. Osipov
September 7, 2020 18:00, Steklov Mathematical Institute, Room. 213 (8 Gubkina)
D. V. Osipov
  
 
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