On some properties of the asymptotic Samuel function

A. Bravo, S. Encinas and J. Guillán‐Rial

Mathematische Nachrichten, 2025, vol. 298, issue 7, 2401-2423

Abstract: The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here, we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

Date: 2025
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https://doi.org/10.1002/mana.12037

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