Extensions of Globally Valued Fields and Arithmetic Geometry

Explore the mathematical framework of globally valued fields and their connections to arithmetic geometry in this research seminar from the Institute for Advanced Study. Learn how globally valued fields serve as a generalization of global fields within the context of first-order continuous logic, and discover their fundamental relationships to key areas of arithmetic geometry including Arakelov geometry, heights, lattices, and adeles. Examine current research findings and open questions concerning extensions of globally valued fields, presented through rigorous mathematical analysis and theoretical exploration. Gain insights into this specialized area of mathematical research that bridges algebraic number theory and geometric approaches to arithmetic problems.