Abstract

In this thesis, we introduce the theory of ´etale cohomology, assuming basics in algebraic
geometry and sheaf theory on topological spaces. In particular, we define ´etale morphisms
and develop the theory of sheaves on the ´etale site alongside some of the most important
examples.
In the last two chapters, we collect, mostly without proofs, some of the most important
results on ´etale cohomology and apply them to outline Deligne’s construction of the Galois
representation attached to a modular form, illustrating the usefulness of that cohomology
theory in number theory.