COMPLETELY CONTROLLING THE DIMENSIONS OF FORMAL FIBER RINGS AT PRIME IDEALS OF SMALL HEIGHT

摘要

Let T be a complete equicharacteristic local (Noetherian) UFD of dimension 3 or greater. Assuming that vertical bar T vertical bar = vertical bar T/m vertical bar, where m is the maximal ideal of T, we construct a local UFD A whose completion is T and whose formal fibers at height one prime ideals have prescribed dimension between zero and the dimension of the generic formal fiber. If, in addition, T is regular and has characteristic zero, we can construct A to be excellent.