Completions of Countable Excellent Rings in Equal Characteristic Zero

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Description
We characterize which complete local rings T containing the rationals are the completion of a countable excellent local ring S. We also discuss the possibilities for the maps from Min(T) to Min(S) and prove some characterization-style results. These results generalize techniques from a recent paper and Teresa Yu's 2020 Williams thesis. We additionally use the same techniques to characterize when a complete local ring B containing the rationals is the completion of an uncountable reduced ring A with a countable prime spectrum and precisely which maps from Min(B) to Min(A) are possible. This result uses techniques from the same recent paper and Teresa Yu's thesis.

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ID Label Size Mimetype Created
OBJ OBJ datastream * 1.17 MiB application/pdf 2022-06-04
TN TN 3.95 KiB image/jpeg 2022-06-04
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