A note on dimension of triangulated categories

In this note we study the behavior of the dimension of the perfect derived category Perf ⁡ ( A ) Perf(A) of a dg-algebra A A over a field k k under a base field extension K / k K/k . In particular, we show that the dimension of a perfect derived category is invariant under a separable algebraic extension K / k K/k . As an application we prove the following statement: Let A A be a self-injective algebra over a perfect field k k . If the dimension of the stable category mod _ A {mod}A is 0 0 , then A A is of finite representation type. This theorem is proved by M. Yoshiwaki in the case when k k is an algebraically closed field. Our proof depends on his result.