Non-archimedean analytic spaces and diophantine geometry

Resumen:

The classical decomposition of height functions as sums of local heights features analytic objects at all places,
complex and p-adic. However, the complex side of this story had a more geometric flavour than the p-adic side,
partly because non-archimedean geometry does not furnish an analogue of the now familiar differential calculus.
I will explain the difficulties that non-archimedean geometry poses and how Berkovich's solution
has remarkable properties that can be exploited towards some differential calculus which is relevant
for diophantine geometry.

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