Height reduction for local uniformization of varieties and non-archimedean spaces

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Abstract

It is known since the works of Zariski that the essential difficulty in the local uniformization problem is met already in the case of valuations of height one. In this paper we prove that local uniformization of schemes and non-archimedean analytic spaces rigorously follows from the case of valuations of height one. For non-archimedean spaces this result reduces the problem to studying local structure of smooth Berkovich spaces.

Original languageAmerican English
Pages (from-to)205-235
Number of pages31
JournalJournal of Algebra
Volume646
DOIs
StatePublished - 15 May 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

  • Berkovich analytic spaces
  • Local desingularization
  • Local uniformization
  • Valuation rings

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