  Given a triangulated category over a field $K$ and a field extension $L/K$,
we investigate how one can construct a triangulated category over $L$. Our
approach produces the derived category of the base change scheme $X_L$ if the
category one starts with is the bounded derived category of a smooth projective
variety $X$ over $K$ and the field extension is finite and Galois. We also
investigate how the dimension of a triangulated category behaves under scalar
extensions.
