Extending valuations to formal completions
F. J. Herrera Govantes, M. A. Olalla Acosta, M. Spivakovsky, B., Teissier
TL;DR
This paper introduces methods for extending valuations from local domains to their formal completions, providing an accessible overview of the authors' detailed joint research on valuation extension theory.
Contribution
It offers an accessible introduction to extending valuations to formal completions, summarizing key ideas without technical complexity.
Findings
Valuations can be extended to formal completions under certain conditions
The paper clarifies the relationship between valuations and formal completions
Provides foundational insights for further research in valuation theory
Abstract
This paper is an extended version of the talk given by Miguel Olalla at the International Conference on Valuation Theory in El Escorial in July 2011. Its purpose is to provide an introduction to our joint paper "Extending a valuation centered in a local domain to the formal completion" (Proc. London Math. Soc. (2012) 105 (3), 571-621) without grinding through all of its technical details.
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