VANISHING OF EXT AND TOR OVER SOME COHEN-MACAULAY LOCAL RINGS

摘要

We discuss vanishing of cohomology of finite modules over Cohen-Macaulay local rings (R, m). Special attention is given to the case when the modules are annihilated by m~2. (Note that if m~3 = 0, then we can assume the modules satisfy this condition.) In this case we obtain effective versions of conjectures of Auslander-Reiten and Tachikawa.