Ian M. Aberbach

activity

20022024

most citedNew estimates of Hilbert-Kunz multiplicities for local rings of fixed dimension

7 citations · 10 across the 17 of their papers we have counts for

collaborators

18 papers

math.AC2024

Bounds for the Hilbert-Kunz Multiplicity of Singular Rings

Ian M. Aberbach, Nicholas O Cox-Steib

In this paper we prove that the Watanabe-Yoshida conjecture holds up to dimension $7$ . Our primary new tool is a function, $φ_{J} (R; z^{t}),$ that interpolates between the H…

math.AC2023

On the Equality of Test Ideals

Ian Aberbach, Craig Huneke, Thomas Polstra

We provide a natural criterion which implies equality of the finitistic test ideal and test ideal in local rings of prime characteristic. Most notably, we show that the criterion i…

math.AC2018

Frobenius Betti numbers and syzygies of finite length modules

Ian M. Aberbach, Parangama Sarkar

Let $(R, m)$ be a local (Noetherian) ring of dimension $d$ and $M$ a finite length $R$ -module with free resolution $G_{∙}$ . De Stefani, Huneke, and Núñez-Betancourt ex…

math.AC2014

Uniform Artin-Rees Bounds for Syzygies

Ian M. Aberbach, Aline Hosry, Janet Striuli

Let $(R, m)$ be a local Noetherian ring, let $M$ be a finitely generated $R$ -module and let $(F_{∙}, \partial_{∙})$ be a free resolution of $M$ . We find a uniform bound $…

math.AC2011★ 7 cited

New estimates of Hilbert-Kunz multiplicities for local rings of fixed dimension

Ian M. Aberbach, Florian Enescu

We present results on the Watanabe-Yoshida conjecture for the Hilbert-Kunz multiplicity of a local ring of positive characteristic. By improving on a "volume estimate" giving a low…

math.AC2010

The Briançon-Skoda Theorem and Coefficient Ideals for Non m-Primary Ideals

Ian M. Aberbach, Aline Hosry

We generalize a Briançon-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\m)$ containing a field, and an ideal $I$ of $R$ …