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math.AC2025
The asymptotic Samuel functions and applications to resolution of singularities techniques
A. Benito, A. Bravo, S. Encinas
We use the asymptotic Samuel function to define the Samuel slope of a Noetherian local ring, and we prove that it characterizes regularity in the case of local excellent rings. In…
math.AC2025
On some properties of the asymptotic Samuel function
A. Bravo, S. Encinas, J. Guillán-Rial
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,…