Forms and currents on the analytification of an algebraic variety (after Chambert-Loir and Ducros)

Abstract

Chambert-Loir and Ducros have recently introduced real differential forms and currents on Berkovich spaces. In these notes, we survey this new theory and we will compare it with tropical algebraic geometry.Comment: 25 pages, notes for my survey talk given at the Simons Symposium in St. John from 1.4-5.4.2013. In the second version, a sign error in the definition of the integral is corrected and the exposition in section 7 is slightly change