Mini-course by Francesco Lemma «Introduction to Shimura varieties»

Abstract: Shimura varieties are algebraic varieties defined over number fields which play a central role in modern arithmetic geometry. One reason for this is that their geometry and cohomology is related to automorphic forms. The most studied Shimura varieties are the ones associated to GL(2). In this case, the set of their complex points is a finite disjoint union of quotients of the upper half-plane by arithmetic subgroups of GL(2). In these lectures we will introduce the axioms defining a Shimura variety and explain in some detail why the Shimura variety associated to the symplectic group GSp(2n) can be seen as a moduli space of abelian varieties.