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 twodimensional
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 twodimensional 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
padic 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. 0751520191614).
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)






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)






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)






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)






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)






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)






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)






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)






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)






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)






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)






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)






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)






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)





