étale site

An étale site is a mathematical framework used in algebraic geometry to study geometric objects called schemes, which generalize algebraic varieties. It involves considering all étale maps—special types of functions that are flat, unramified, and resemble local isomorphisms—between schemes. These maps form a "category" with a topology, allowing mathematicians to analyze schemes locally, similarly to how open sets work in topology. This approach helps in understanding properties that are preserved under these special maps, enabling deeper insights into the structure and behavior of algebraic geometric objects.