ScalingStacks

Remark 3.4. Given a continuous metric $\left\lVert\cdot\right\rVert$, one can assign to it a ‘closed (1,1)-form’ $\theta$, which for model metrics roughly amounts to taking the numerical class of the model line bundle. This is a formal analogue for the curvature form of a Hermitian metric. For instance, $\left\lVert\cdot\right\rVert e^{-\phi}$ is a continuous semipositive metric iff the potential $\phi$ is a continuous $\theta$-psh function. Another theory of forms and currents on Berkovich spaces is developed by Chambert-Loir and Ducros [12], which is closer in spirit to differential calculus.