$\mathfrak{m}$-adic Perturbations in Noetherian Local Rings

Abstract

We develop new methods to study $\mathfrak{m}$-adic stability in an arbitrary Noetherian local ring. These techniques are used to prove results about the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities under fine $\mathfrak{m}$-adic perturbations.

arXiv comment46 pages. Feedback is welcome! Version 2: improved introduction and references

References in corpus (1)

• Stability and deformation of F-singularities