Descent theory is a framework in algebraic geometry that studies how objects (like schemes) can be related to each other through a process of pulling back along morphisms and understanding how these relationships behave under various conditions. This theory is crucial for understanding the gluing of local data into global structures, often explored through the lens of topos theory. It provides insights into how local geometric properties can be extended to a global context, making it essential for applications in both algebraic geometry and number theory.
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