Scalar Extensions of Triangulated Categories

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