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Patching on analytic fibers and local-global principles

Abstract
Patching techniques have become an important tool for proving local-global principles over function fields of curves. These principles provide a way to study the existence of rational points on varieties. I will explain how using non-archimedean analytic spaces and patching techniques on them one obtains an approach to local-global principles in higher dimensional settings. The talk will begin with a brief introduction of the objects that will be used.