Many results in real algebraic geometry are proved by passing from a real variety to its complexification , then studying the action of complex conjugation on . For example, one often regards $X(\mathbb R)$ as the fixed-point locus of conjugation on $X(\mathbb C)$. This appears in results such...

If $f \colon X \to Y$ is a finite surjective morphism between integral Noetherian schemes, then the set $V\subseteq Y$ of points over which $f$ is flat is open. I want to show that this fails if we drop the finiteness assumption. I can think of an example given by blowing up $\mathbb A^3$ at a...