Chains of Unusual Excellent Local Rings
Kai Chen
Abstract
Let (T,M) be a complete local domain containing the integers. Let p1 ⊂eq p2 ⊂eq ... ⊂eq pn be a chain of nonmaximal prime ideals T such that Tpn is a regular local ring. We construct a chain of excellent local domains An ⊂eq A1 such that for each i, the completion of Ai is T, the generic formal fiber of Ai is local with maximal ideal pi, and if I is a nonzero ideal of Ai then Ai/I is complete. Consequently, if in addition T is a UFD, then we can construct a chain of excellent local UFDs satisfying the same conditions.
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