1 citations · 1 across the 8 of their papers we have counts for
9 papers
Regular rings over valuation rings
Shiji Lyu
Bertin (1972) defined regularity for coherent local rings, and Knaf (2004) studied the property for a local ring essentially finitely presented over a valuation ring . We di…
-ifications, semi-Nagata rings, and the lifting problem
Shiji Lyu
This is a two-part article. In the first part, we study an alternative notion to Nagata rings. A Nagata ring is a Noetherian ring such that every finite -algebra that is an…
Uniform bounds in excellent -algebras and applications to semi-continuity
Shiji Lyu, Cheng Meng
We study two important numerical invariants, Hilbert--Kunz multiplicity and -signature, on the spectrum of a Noetherian -algebra that is not necessarily -fi…
The Japanese and universally Japanese properties for valuation rings and Prüfer domains
Shiji Lyu
We discuss the Japanese and universally Japanese properties for valuation rings and Prüfer domains. These properties, regarding finiteness of integral closure, have been studied ex…
Formal lifting of dualizing complexes and consequences
Shiji Lyu
We show that for a Noetherian ring that is -adically complete for an ideal , if admits a dualizing complex, so does . This gives an alternative proof of the fact…
On some properties of birational derived splinters
Shiji Lyu
A Noetherian reduced ring is called a birational derived splinter if for all proper birational maps , the canonical map spl…
The gamma-construction and permanence properties of the (relative) -rational signature
Shiji Lyu
We study some permanence properties of the relative -rational signature defined and studied by Smirnov--Tucker. We show that this invariant is compatible with the gamma-construc…
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero
Shiji Lyu, Takumi Murayama
We establish the relative minimal model program with scaling for locally projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent for…
Permanence properties of splinters via ultrapower
Shiji Lyu
We show that the splinter property ascends along regular residue field extensions, and along arbitrary regular maps in equal characteristic. We also study the splinter property of…