Espaces de Berkovich, geometrie et dynamique – Berko

Berkovich theory furnishes a general setting which allows one to talk about analytic varieties defined over arbitrary metrized fields while keeping good topological properties such as local connectedness and compactness. Introduced at the end of the 80's, this geometry has since then found numerous applications in a variety of domains including p-adic analysis, arithmetic geometry and holomorphic dynamics. Our project put together young french researchers working on these spaces or simply using them as a tool. Our research plan include three main directions: first a contribution to the development of foundational aspects of the theory (study of morphisms, cohomological theories, potential theory); then a focus on nonarchimedean dynamical systems for which Berkovich spaces constitute the natural phase space; lastly we wish to study the relationship between complex geometry and Berkovich geometry (compactification of moduli space of polynomials, degeneracy of Hodge structures, links of the space of arcs)