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.

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- Last edited by Andrew Sutherland on 2020-10-10 14:57:18

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- 2020-10-10 14:57:18 by Andrew Sutherland (Reviewed)
- 2020-10-10 14:50:47 by Andrew Sutherland
- 2017-05-24 05:30:10 by Christelle Vincent (Reviewed)

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