41 citations · 191 across the 44 of their papers we have counts for
49 papers
Perfectoid Pure and Signature Pairs
Hanlin Cai, Anne Fayolle, Linquan Ma +4
We extend perfectoid purity and related invariants to divisor pairs in mixed characteristic. The resulting purity condition agrees with -purity of pairs in characteristic as…
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…
Local cohomological dimension and depth in mixed characteristic
Linquan Ma
Let be an unramified regular local ring of mixed characteristic and dimension and let be an ideal. We prove that imp…
Herzog ideals and -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 -singularities. More precisely, we show that, in positive c…
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 is an -generated ideal in any ring . We prove a general Briançon-Skoda-type containment relating the integral closure w…
Lech-Mumford constant and stability of local rings
Linquan Ma, Ilya Smirnov
We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new exampl…
On complete integral closedness of the -adic completion of absolute integral closure
Raymond Heitmann, Linquan Ma
Fix a prime and let be a Noetherian complete local domain of mixed characteristic with fraction field . Let denote the absolute integral clo…
Perfectoid pure singularities
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +4
Fix a prime number . Inspired by the notion of -pure or -split singularities, we study the condition that a Noetherian ring with in its Jacobson radical is pure inside…
Test ideals in mixed characteristic: a unified theory up to perturbation
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +5
Let be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inver…
Colength, multiplicity, and ideal closure operations II
Linquan Ma, Pham Hung Quy, Ilya Smirnov
Let be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert--Samuel or…
Vanishing and non-negativity of the first normal Hilbert coefficient
Linquan Ma, Pham Hung Quy
Let be a Noetherian local ring such that is reduced. We prove that, when is , if there exists a parameter ideal s…
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 -signature and Hilbert-Kunz multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' norma…
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…
Uniform Lech's inequality
Linquan Ma, Ilya Smirnov
Let be a Noetherian local ring of dimension . We prove that if , then the classical Lech's inequality can be improved uniformly…
A Buchsbaum theory for tight closure
Linquan Ma, Pham Hung Quy
A Noetherian local ring is called Buchsbaum if the difference , where is an ideal generated by a system o…
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…
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 . The focus is on complexes that have length , wh…
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 that admit secondary representations of which are stable under the natur…
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 of Noetherian local rings, we have an inequ…
Koszul and local cohomology, and a question of Dutta
Linquan Ma, Anurag K. Singh, Uli Walther
For a local ring of dimension , we study the natural map from the Koszul cohomology module to the local cohomology module $H^n_\mathfra…
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 and we have . Over a regular ring, a result by Ein-Lazarsf…
An analog of adjoint ideals and PLT singularities in mixed characteristic
Linquan Ma, Karl Schwede, Kevin Tucker +2
We use the framework of perfectoid big Cohen-Macaulay algebras to define a class of singularities for pairs in mixed characteristic, which we call purely BCM-regular singularities,…
Covers of rational double points in mixed characteristic
Javier Carvajal-Rojas, Linquan Ma, Thomas Polstra +2
We further the classification of rational surface singularities. Suppose is a strictly Henselian regular local ring of mixed characteristic $(0, p…
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 -primary ideal in a Noetherian local ring .…