Fedor Bogomolov

Many problems in the study of complex algebraic varieties can be reduced to the study of algebraic varieties over the fields of finite characteristics. For example the only existing proof of the Mori theorem on the existence of rational curves is based on reduction to finite characteristics. In fact most of the questions in complex algebraic geometry can be reduced to the case of study of varieties over finite fields where additional finiteness arguments apply. In this talk I will discuss the structure of projective curves of higher genus defined over finite fields considered as a subset of their jacobian variety.