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Something seems to be missing in the sentence

There is an example of a regular local ring A of dimension 1 and characteristic p>0 which is not excellent. If k is any field of characteristic p with [k:k∞] and R=k x and A is the subring of power series Σaixi such that [kp(a0,a1,...):kp ] is finite then the formal fibers of A are not all geometrically regular so A is not excellent.

Also, what is the definition of k∞ ? Arcfrk 05:07, 26 March 2007 (UTC) reply

• give counterexamples, checkout https://arxiv.org/abs/1704.03628
• https://mathoverflow.net/questions/194134/excellent-schemes
• Give intuition for why they matter