p-adic Geometry
p-adic Geometry is a branch of mathematics that studies geometric structures using the p-adic numbers. These numbers extend the traditional number system by focusing on divisibility by a prime number p. In this framework, distances and shapes are analyzed in a way that differs from classical geometry, allowing for unique insights into number theory and algebraic geometry.
In p-adic Geometry, points and curves are examined through the lens of p-adic metrics, which measure how close numbers are based on their p-adic expansions. This approach reveals properties of solutions to polynomial equations and helps mathematicians understand the behavior of numbers in a new context, bridging gaps between various mathematical disciplines.