Formes diff\'erentielles r\'eelles et courants sur les espaces de   Berkovich
  We define a theory of real $(p,q)$-forms and currents on Berkovich spaces which is parallel to the theory of differential forms on complex spaces: integrals, Poincar\'e-Lelong formula, plurisubharmonic functions, positive currents, Chern forms of metrized line bundles... 
Antoine Chambert-Loir, Antoine Ducros
math.AG math.NT