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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.…