In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1] Arithmetic geometry is centered around …

What is arithmetic geometry? Algebraic geometry studies the set of solutions of a multivariable polynomial equation (or a system of such equations), usually over R or C.

Abstract. This article surveys a few of the highlights in the arithmetic of curves: the proof of the Mordell Conjecture, and the more detailed theory that has developed around the classes of …

May 7, 2023 · Since an affine variety in this context is given by solutions to Diophantine equations, this is also called Diophantine geometry. An archetypical application of arithmetic …

This book contains the proceedings of the International Colloquium on Arithmetic Geometry organized by the Tata Institute of Fundamental Research in January 2020, one of a series of …

Jun 13, 2025 · The intersection of algebraic geometry and number theory gives rise to arithmetic geometry. This field seeks to understand the arithmetic properties of geometric objects, such …

This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical …