Linquan Ma

activity

20122026

most citedPerfectoid multiplier/test ideals in regular rings and bounds on symbolic powers

41 citations · 191 across the 44 of their papers we have counts for

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41 papers · 1 filter

math.AC2026

Counterexamples to Peskine-Szpiro's conjecture on modules of finite projective dimension

Linquan Ma

We give counterexamples to the remaining homological conjectures of Peskine-Szpiro concerning modules of finite projective dimension over Noetherian local rings. Specifically, we s…

math.AC2026

Local cohomological dimension and depth in mixed characteristic

Linquan Ma

Let $(R, m)$ be an unramified regular local ring of mixed characteristic $(0, p)$ and dimension $d$ and let $I \subseteq R$ be an ideal. We prove that $d e pt h (R / I) \geq 3$ imp…

math.AC2026

Herzog ideals and $F$ -singularities

Alessandro De Stefani, Linquan Ma, Matteo Varbaro

In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and $F$ -singularities. More precisely, we show that, in positive c…

math.AC2025

The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

Linquan Ma, Peter M. McDonald, Rebecca R. G. +1

Suppose $J = (f_{1}, \dots, f_{n})$ is an $n$ -generated ideal in any ring $R$ . We prove a general Briançon-Skoda-type containment relating the integral closure $J^{n + k - 1}$ w…

math.AC2025

On complete integral closedness of the $p$ -adic completion of absolute integral closure

Raymond Heitmann, Linquan Ma

Fix a prime $p$ and let $(R, m)$ be a Noetherian complete local domain of mixed characteristic $(0, p)$ with fraction field $K$ . Let $R^{+}$ denote the absolute integral clo…

math.AC2023

Colength, multiplicity, and ideal closure operations II

Linquan Ma, Pham Hung Quy, Ilya Smirnov

Let $(R, m)$ be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert--Samuel or…

math.AC2023

Vanishing and non-negativity of the first normal Hilbert coefficient

Linquan Ma, Pham Hung Quy

Let $(R, m)$ be a Noetherian local ring such that $R$ is reduced. We prove that, when $R$ is $S_{2}$ , if there exists a parameter ideal $Q \subseteq R$ s…

math.AC2022★ 2 cited

Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups

Hanlin Cai, Seungsu Lee, Linquan Ma +2

We define a (perfectoid) mixed characteristic version of $F$ -signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' norma…

math.AC2022

Lim Ulrich sequences and Boij-Söderberg cones

Srikanth B. Iyengar, Linquan Ma, Mark E. Walker

This paper extends the results of Boij, Eisenbud, Erman, Schreyer, and Söderberg on the structure of Betti cones of finitely generated graded modules and finite free complexes over…

math.AC2022

Uniform Lech's inequality

Linquan Ma, Ilya Smirnov

Let $(R, m)$ be a Noetherian local ring of dimension $d \geq 2$ . We prove that if $e (R_{r e d}) > 1$ , then the classical Lech's inequality can be improved uniformly…

math.AC2021

A Buchsbaum theory for tight closure

Linquan Ma, Pham Hung Quy

A Noetherian local ring $(R, m)$ is called Buchsbaum if the difference $e (q, R) - ℓ (R / q)$ , where $q$ is an ideal generated by a system o…

math.AC2021

Maximal Cohen-Macaulay complexes and their uses: A partial survey

Srikanth B. Iyengar, Linquan Ma, Karl Schwede +1

This work introduces a notion of complexes of maximal depth, and maximal Cohen-Macaulay complexes, over a commutative noetherian local ring. The existence of such complexes is clos…

math.AC2021★ 6 cited

Multiplicities and Betti numbers in local algebra via lim Ulrich points

Srikanth B. Iyengar, Linquan Ma, Mark E. Walker

This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$ . The focus is on complexes that have length $dim R$ , wh…

math.AC2020★ 1 cited

F-stable secondary representations and deformation of F-injectivity

Alessandro De Stefani, Linquan Ma

We prove that deformation of F-injectivity holds for local rings $(R, m)$ that admit secondary representations of $H_{m}^{i} (R)$ which are stable under the natur…

math.AC2020★ 1 cited

Lim Ulrich sequences and Lech's conjecture

Linquan Ma

The long standing Lech's conjecture in commutative algebra states that for a flat local extension $(R, m) \to (S, n)$ of Noetherian local rings, we have an inequ…

math.AC2020

Koszul and local cohomology, and a question of Dutta

Linquan Ma, Anurag K. Singh, Uli Walther

For a local ring $(A, m)$ of dimension $n$ , we study the natural map from the Koszul cohomology module $H^{n} (m; A)$ to the local cohomology module $H^n_\mathfra…

math.AC2019

Symbolic power containments in singular rings in positive characteristic

Eloísa Grifo, Linquan Ma, Karl Schwede

The containment problem for symbolic and ordinary powers of ideals asks for what values of $a$ and $b$ we have $I^{(a)} \subseteq I^{b}$ . Over a regular ring, a result by Ein-Lazarsf…

math.AC2019

Asymptotic Lech's inequality

Craig Huneke, Linquan Ma, Pham Hung Quy +1

We explore the classical Lech's inequality relating the Hilbert--Samuel multiplicity and colength of an $m$ -primary ideal in a Noetherian local ring $(R, m)$ .…

math.AC2019★ 1 cited

Filter regular sequence under small perturbations

Linquan Ma, Pham Hung Quy, Ilya Smirnov

We answer affirmatively a question of Srinivas--Trivedi: in a Noetherian local ring $(R, m)$ , if $I = (f_{1}, \dots, f_{r})$ is an ideal generated by a filter-regular sequence an…

math.AC2019

Colength, multiplicity, and ideal closure operations

Linquan Ma, Pham Hung Quy, Ilya Smirnov

In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then $R$ is regular. We deduce this using the relationship betwee…

math.AC2019★ 6 cited

Regularity, singularities and $h$ -vector of graded algebras

Hailong Dao, Linquan Ma, Matteo Varbaro

Let $R$ be a standard graded algebra over a field. We investigate how the singularities of $R$ affect its $h$ -vector, which is the coefficients of the numerator of its Hilbert seri…

math.AC2018★ 1 cited

A Kunz-type characterization of regular rings via alterations

Linquan Ma, Karl Schwede

We prove that a local domain $R$ , essentially of finite type over a field, is regular if and only if for every regular alteration $π : X \to S p ec R$ , we have that $R π_* \mathcal{O}…

math.AC2018★ 1 cited

Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology

Patricia Klein, Linquan Ma, Pham Hung Quy +2

Let $(R, m)$ be a Noetherian local ring, and let $M$ be a finitely generated $R$ -module of dimension $d$ . We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…

math.AC2018★ 24 cited

Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras

Linquan Ma, Karl Schwede

We utilize recent results of André and Gabber on the existence of weakly functorial integral perfectoid big Cohen-Macaulay (BCM) algebras to study singularities of local rings in m…

Counterexamples to Peskine-Szpiro's conjecture on modules of finite projective dimension

Local cohomological dimension and depth in mixed characteristic

Herzog ideals and F-singularities

The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

On complete integral closedness of the p-adic completion of absolute integral closure

Colength, multiplicity, and ideal closure operations II

Vanishing and non-negativity of the first normal Hilbert coefficient

Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups

Lim Ulrich sequences and Boij-Söderberg cones

Uniform Lech's inequality

A Buchsbaum theory for tight closure

Maximal Cohen-Macaulay complexes and their uses: A partial survey

Multiplicities and Betti numbers in local algebra via lim Ulrich points

F-stable secondary representations and deformation of F-injectivity

Lim Ulrich sequences and Lech's conjecture

Koszul and local cohomology, and a question of Dutta

Symbolic power containments in singular rings in positive characteristic

Asymptotic Lech's inequality

Filter regular sequence under small perturbations

Colength, multiplicity, and ideal closure operations

Regularity, singularities and h-vector of graded algebras

A Kunz-type characterization of regular rings via alterations

Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology

Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras

Herzog ideals and $F$ -singularities

On complete integral closedness of the $p$ -adic completion of absolute integral closure

Regularity, singularities and $h$ -vector of graded algebras