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).

Lecturer
Shabat Georgii Borisovich

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