Abstract: A conjecture of Nisnevich predicts that for a smooth variety X over a field, a smooth divisor D in X, and a totally isotropic reductive X-group scheme G, every generically trivial G-torsor on X \ D trivializes Zariski locally on X. I will discuss this conjecture and related questions about torsors under reductive groups over regular rings.
Ref: K.Cesnavivius, The Bass-Quillen phenomenon for reductive group torsors
