Chains of Unusual Excellent Local Rings

Details Chains of Unusual Excellent Local Rings Chains of Unusual Excellent Local Rings

2003-11-18

arxiv.org/abs/math/0311317v1

Mathematics

Commutative Algebra

10 pages

Scientific paper

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.

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