Base change (reviewed)

Let $V$ be an algebraic variety defined over a field $K$. If $L/K$ is a field extension, then any set of equations that define $V$ over $K$ can be used to define an algebraic variety over $L$, the base change of $V$ from $K$ to $L$ (typically denoted $V_L$).

An algebraic variety over a field $L$ is said to be a base change if it is the base change of an algebraic variety defined over a proper subfield of $L$, equivalently, if its base field is not a minimal field of definition.