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Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer ...
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Lecture notes from the summer school "Ad- vanced Course on Integral Geometry and Valuation Theory", CRM Barcelona, 2010. Pub- lished as Chapter 2 in: Advanced Courses in Mathematics CRM Barcelona, Integral Geom- etry and Valuations, E. Gallego and G. Solanes (editors), Springer, Basel, ...