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Published online by Cambridge University Press: 06 October 2022
This is an expository account about height functions and Arakelov theory in arithmetic geometry. We recall Conrad’s description of generalized global fields in order to describe heights over function fields of higher transcendence degree. We then give a brief overview of Arakelov theory and arithmetic intersection theory. Our exposition culminates in a description of Moriwaki’s Arakelov-theoretic formulation of heights, as well as a comparison of Moriwaki’s construction to various versions of heights.
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