Nilpotent thickening
= Nilpotent thickening
A nilpotent thickening is a <closed immersion> defined by a nilpotent <ideal sheaf of a closed subscheme>. Its underlying topological map is a <homeomorphism>, because every <prime ideal> contains every <nilpotent element>. For example, quotienting the <dual numbers> by $(\varepsilon)$ changes the <structure sheaf> without changing the single point of the spectrum.