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Course by G. B. Shabat "Arithmetic surfaces"
(September 12–December 12, 2022, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online)
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The main definitions, related to Grothendieck schemes and their morphisms will be given, formalizing the intuitive concept of a "family of curves". Curves over fields of algebraic numbers will be interpreted as families of curves over the rings of integers of these fields. Special attention will be paid to families of elliptic curves. An introduction to Arakelov geometry will be given in terms of a completion of an arithmetic surface.
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. 075-15-2022-265).
 Program
Lecturer
Shabat Georgii Borisovich
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
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| Course by G. B. Shabat "Arithmetic surfaces", September 12–December 12, 2022 |
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December 12, 2022 (Mon) |
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| 1. |
Lecture 11. Arithmetic surfaces
G. B. Shabat
December 12, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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November 28, 2022 (Mon) |
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| 2. |
Lecture 10. Arithmetic surfaces
G. B. Shabat
November 28, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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November 21, 2022 (Mon) |
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| 3. |
Lecture 9. Arithmetic surfaces
G. B. Shabat
November 21, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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November 14, 2022 (Mon) |
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| 4. |
Lecture 8. Arithmetic surfaces
G. B. Shabat
November 14, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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October 31, 2022 (Mon) |
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| 5. |
Лекция 7. Арифметические поверхности
G. B. Shabat
October 31, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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October 24, 2022 (Mon) |
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Lecture 6. Arithmetic surfaces
G. B. Shabat
October 24, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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October 17, 2022 (Mon) |
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| 7. |
Lecture 5. Arithmetic surfaces
G. B. Shabat
October 17, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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October 10, 2022 (Mon) |
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| 8. |
Lecture 4. Arithmetic surfaces
G. B. Shabat
October 10, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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October 3, 2022 (Mon) |
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| 9. |
Lecture 2. Arithmetic surfaces
G. B. Shabat
October 3, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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September 26, 2022 (Mon) |
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| 10. |
Lecture 3. Arithmetic surfaces
G. B. Shabat
September 26, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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September 12, 2022 (Mon) |
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| 11. |
Lecture 1. Arithmetic surfaces
G. B. Shabat
September 12, 2022 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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