coherent sheaves

Coherent sheaves are mathematical tools used in algebraic geometry to study geometric objects like shapes and spaces through algebraic data. Think of them as systematic ways to track information, such as functions or sections, across different parts of a space, ensuring this data behaves consistently and has manageable complexity. They generalize the idea of functions on shapes, allowing mathematicians to understand both local properties (small regions) and global structure simultaneously. Coherent sheaves enable precise articulation of how local details fit together to form the overall geometry, bridging algebraic and geometric perspectives.