Global analytic geometry is a developing subject that gives an alternative/complementary approach to scheme theory in arithmetic geometry and analytic number theory?. The starting point of this theory is in Vladimir Berkovich’s book about spectral theory and non-archimedean analytic geometry. It was then developped further by Jerome Poineau.
The main aim of this theory is to define, using global analytic tools, a good category of analytic motivic coefficients, that would help in proving naturally:
Argument in favor of its use are:
(to be expanded)
A short introduction for large audience can be found in the following article of the EMS newsletter:
Jerome Poineau: Global analytic geometry
Frédéric Paugam, Global analytic geometry and the functional equation (lecture notes)
Jerome Poineau: [La droite de Berkovich sur Z], Asterisque 334 (2010). (fundamental properties of the affine line)
Jerome Poineau: Espaces de Berkovich sur Z: etude locale. (coherence of the sheaf of analytic functions on higher dimensional affine spaces)