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20182026
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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 be an unramified regular local ring of mixed characteristic and dimension and let be an ideal. We prove that imp…

math.AC2025

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…

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.AC2020

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…

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 -primary ideal in a Noetherian local ring .…