Chains of Unusual Excellent Local Rings

Publication date: 18 November 2003

Abstract: Let (T,M) be a complete local domain containing the integers. Let p1 subseteq p2 subseteq ... subseteq pn be a chain of nonmaximal prime ideals T such that T_pn is a regular local ring. We construct a chain of excellent local domains An subseteq 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.

Mathematics Subject Classification ID

Complete rings, completion (13J10) Power series rings (13J05)

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