Abstract:  

I will present results from a joint work with Itaï Ben Yaacov, Pablo Destic and Ehud Hrushovski, where we lay foundations of globally valued fields and relate them to Arakelov geometry and to Banach lattices. Globally valued fields (abbreviated GVF) are a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We give a representation theorem, saying that on a countable fields, every GVF structure comes from a proper adelic curve, as defined by Chen and Moriwaki. If time permits, I will talk about some applications from a joint work with Pablo Destic and Nuno Hultberg.

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