3 citations · 10 across the 9 of their papers we have counts for
9 papers
The Bass--Quillen conjecture for torsors over valuation rings
Ning Guo, Fei Liu
For a valuation ring , a smooth -algebra , and a reductive -group scheme satisfying a certain natural isotropicity condition, we prove that every Nisnevich -tors…
On the Grothendieck--Serre conjecture for projective smooth schemes over a DVR
Ning Guo, Ivan Panin
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme over a regular local ring is trivial. The mixed characteris…
A presentation theorem for smooth projective schemes over discrete valuation rings
Ning Guo, Ivan Panin
In this article, we give a proof for a geometric presentation theorem for any irreducible scheme smooth projective over a discrete valuation ring . As a consequence, for any…
Purity and quasi-split torsors over Prüfer bases
Ning Guo, Fei Liu
We establish an analogue of the Zariski--Nagata purity theorem for finite étale covers on smooth schemes over Prüfer rings by demonstrating Auslander's flatness criterion in this n…
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.…
Divisors on coherent schemes and homogeneous spaces
Ning Guo
We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classic…
The Grothendieck--Serre conjecture over valuation rings
Ning Guo
In this article, we establish the Grothendieck-Serre conjecture over valuation rings: for a reductive group scheme over a valuation ring with fraction field , a -tors…
Inverse scattering transform for the Kundu-Eckhaus Equation with nonzero boundary condition
Ning Guo, Jian Xu
In this paper, we consider the initial value problem for both of the defocusing and focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions (NZBCs) at infinity by in…
Wildly Compatible Systems and Six Operations
Ning Guo
For a scheme separated and of finite type over an excellent regular scheme , we define wildly compatible systems of constructible sheaves of modules over finite fields on $X…