Arithmetic of Shimura Varieties

Abstract

Arithmetic properties of Shimura varieties are an exciting topic which has roots in classical topics of algebraic geometry and of number theory such as modular curves and modular forms. This very active research field has contributed to some of the most spectacular developments in number theory and arithmetic geometry in the last twenty years. Shimura varieties and their equal characteristic analogue, moduli spaces of shtukas, are closely related to the Langlands program (classical as well as $p$-adic). A particular case is given by moduli spaces of abelian varieties, a classical object of study in algebraic geometry.