Derived equivalence as iterated tilting

Abstract.

Let A and B be two finite dimensional algebras derived equivalent to a connected hereditary noetherian category $\cal H$ with a tilting complex. We prove that there exists a sequence of finite dimensional algebras $\Lambda _0, \Lambda _1,\ldots ,\Lambda _m$ and tilting modules $T_{\Lambda _0},T_{\Lambda _1},\ldots ,T_{\Lambda _{m-1}}, m\geqq 1$, such that $\Lambda _0=A, \Lambda _m= B$, and $\Lambda _{i+1}= {\rm End}\, {T\!}_{A_i}$ for $0 \leqq i \le m$.