This monograph contributes to the foundations of the theory of global Berkovich spaces. This recent approach of analytic geometry, which blends the known theories of complex and -adic analytic spaces, provides a natural geometric framework for several arithmetic theories, such as Arakelov geometry. The authors focus on three main themes which have yet to be investigated beyond dimension 1 : category, topology, and cohomology. In particular, they introduce a notion of overconvergent affinoid domain where the analogues of Tate's and Kiehl's theorems hold. weiterlesen