Appears in collection : Model Theory and Applications

Chambert-Loir and Ducros have recently developed a theory of real differential forms, integration and currents on Berkovich spaces which is parallel to the the classical theory of differential forms on complex spaces. We will report on joint work with Ducros and Hrushovski, showing that such non-archimedean forms and integrals arise naturally as limits of their archimedean counterparts when one studies the asymptotic behaviour of families of complex varieties on the punctured disc.