41 citations · 191 across the 44 of their papers we have counts for
7 papers · 1 filter
A Kunz-type characterization of regular rings via alterations
Linquan Ma, Karl Schwede
We prove that a local domain , essentially of finite type over a field, is regular if and only if for every regular alteration , we have that $R π_* \mathcal{O}…
-signature under birational morphisms
Linquan Ma, Thomas Polstra, Karl Schwede +1
We study -signature under proper birational morphisms , showing that -signature strictly increases for small morphisms or if . In certain cases,…
Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology
Patricia Klein, Linquan Ma, Pham Hung Quy +2
Let be a Noetherian local ring, and let be a finitely generated -module of dimension . We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…
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…
Cohomologically full rings
Hailong Dao, Alessandro De Stefani, Linquan Ma
Inspired by a question raised by Eisenbud-Mustaţă-Stillman regarding the injectivity of maps from modules to local cohomology modules and the work by the third author w…
Maximal Cohen-Macaulay modules over certain Segre products
Linquan Ma
We prove some results on the non-existence of rank one maximal Cohen-Macaulay modules over certain Segre product rings. As an application we show that over these Segre product ring…
Regular rings and perfect(oid) algebras
Bhargav Bhatt, Srikanth B. Iyengar, Linquan Ma
We prove a -adic analog of Kunz's theorem: a -adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is d…