Chains of Unusual Excellent Local Rings
نویسنده
چکیده
Let (T,M) be a complete local domain containing the integers. Let p1 ⊆ p2 ⊆ · · · ⊆ pn be a chain of nonmaximal prime ideals of T such that Tpn is a regular local ring. We construct a chain of excellent local domains An ⊆ An−1 ⊆ · · · ⊆ A1 such that for each 1 ≤ i ≤ n, 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, we can construct a chain of excellent local UFDs An ⊆ An−1 ⊆ · · · ⊆ A1 satisfying the same conditions.
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