ag.algebraic geometry - What is the base change in number theory?

In number theory, base change of a scheme or a variety is with respect to the underlying ring or field, is viewing the same scheme/variety over an extended ring or field, but with the "same" set of equations.

For example given a curve over $mathbb Q$, it is also a curve over any number field. Or given a scheme over spectrum of $mathbb Z$ given by some equation, you can reduce it modulo a prime $p$ and obtain a scheme over $mathbb F_p$.

When you are dealing with group schemes, moduli, motives, etc., such notions carry over through base change, modulo technical details.