Fei Liu

collaborators

3 papers

math.AG2026

The unramified Grothendieck--Serre conjecture

Fei Liu

We prove that a generically trivial torsor under a reductive group scheme over an unramified regular local ring is trivial.

math.AG2025

The Bass--Quillen conjecture for torsors over valuation rings

Ning Guo, Fei Liu

For a valuation ring $V$ , a smooth $V$ -algebra $A$ , and a reductive $V$ -group scheme $G$ satisfying a certain natural isotropicity condition, we prove that every Nisnevich $G$ -tors…

math.AG2023

Grothendieck--Serre for constant reductive group schemes

Ning Guo, Fei Liu

The Grothendieck--Serre conjecture predicts that on a regular local ring there is no nontrivial torsor under a reductive group scheme that becomes trivial over the fraction field.…