Homological Invariants over Local Rings

In this chapter we are concerned with homological invariants of complexes over local rings. The transition to commutative Noetherian rings allowed us in Sects. 12.1–12.3 and 15.4 to restate several results from Parts I and II in a simpler or stronger form. There are similar gains to be reaped when one focuses on local rings, and many of them are recorded in Sects. 16.1 and 16.2. Firstly though,we recall some terminology and facts that are particular to the local situation; again, they may be found in [207] or any other standard reference on commutative algebra.