It is shown that the derived dimension of any representation-finite Artin algebra is at most one. Mathematics Subject Classification 2000: 16G10, 18E30, 18E10. Let T be a triangulated category, and I and J two full subcategories of T . Denote by 〈I〉 the smallest full subcategory of T containing I and closed under shifts, finite direct sums and direct summands. Denote by I∗J the full subcategory...

0→ Ps → · · · → Pi → 0 where each Pi is a finitely generated projective R-module. Let P the full subcategory of D consisting of complexes isomorphic to perfect complexes. These are precisely the compact objects, also called small objects, in D. These notes are an abstract of two lectures I gave at the workshop. The main goal of the lectures was to present various proofs of a theorem of Hopkins ...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...