activity
20242026
most citedThe relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero

1 citations · 1 across the 3 of their papers we have counts for

collaborators

7 papers

math.AC2026

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…

math.AC2026

-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…

math.AG20261 cited

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…

math.AC2025

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 e…

math.AC2025

Uniform bounds in excellent -algebras and applications to semi-continuity

Shiji Lyu

We study two important numerical invariants, Hilbert--Kunz multiplicity and -signature, on the spectrum of a Noetherian -algebra that is not necessarily -fi…

math.AC2024

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…