Depending on your point of view, Shimura varieties are a special kind of locally symmetric
spaces, a generalization of moduli spaces of abelian schemes with extra structures, or the
imperfect characteristic 0 version of moduli spaces of shtuka. They play an important role
in the Langlands program because they have many symmetries (the Hecke correspondences)
allowing us to link their cohomology to the theory of automorphic represnetations, and on
the other hand they are explicit enough for this cohomology to be computable. The goal of
these lectures is to give an introduction to Shimura varieties, to present some examples, and
to explain the conjectures on their cohomology (at least in the simplest case).
Sophie Morel (ENS Lyon)
11 июл 2022
