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Abstract
We generalize Zariski's Perron transforms to obtain a proof of local uniformization of an arbitrary singular variety of characteristic zero along a valuation of arbitrary rank. Furthermore, we resolve the centers of all the composite valuations as well as the prime ideals of infinite value.
ACKNOWLEDGMENTS
The author sincerely thanks Cutkosky for suggesting the problem and for many helpful discussions concerning the material in this article. The author would like to thank the referee for all the suggestions and insightful remarks.
Notes
Communicated by I. Swanson.