adelic points

Adelic points are a way to study solutions to equations in number theory by considering all possible completions of a number field simultaneously. Imagine examining solutions over the usual real numbers and all possible "p-adic" number systems (which relate to prime numbers). Combining these perspectives gives the adelic points, providing a unified framework that captures local solutions at every prime and at infinity. This approach helps mathematicians understand the global structure of solutions and their behavior across different number systems, offering a comprehensive picture of the solutions' properties.