D-modules

D-modules are mathematical objects used to study differential equations and their solutions within algebraic geometry. Think of them as a framework that combines functions and their derivatives, allowing mathematicians to analyze how functions behave under differentiation in a highly structured way. This approach helps to understand the relationships between solutions of differential equations, especially in complex geometric settings. In essence, D-modules provide a powerful language to unify algebraic and differential perspectives, enabling deep insights into the behavior of systems described by differential operators across various mathematical spaces.