A NOTE ON DIMENSION OF TRIANGULATED CATEGORIES

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