Cet ouvrage propose une contribution aux fondements de la théorie des espaces de Berkovich globaux. Cette approche récente à la géométrie analytique, qui mêle les théories classiques des espaces analytiques complexes et p-adiques, fournit un cadre géométrique naturel pour plusieurs théories arithmétiques, telle que la théorie d'Arakelov. Les auteurs suivent trois axes principaux, inexplorés au-delà de la dimension 1: catégorie, topologie et cohomologie. En particulier, ils introduisent une notion de domaine affinoïde surconvergent, pour lequel sont valables les analogues des théorèmes de Tate et de Kiehl.
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
p-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.
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