Relative A 1-Contractibility of Koras-Russell Prototypes and Exotic Motivic Spheres
The paper extends A1-contractibility from Koras-Russell threefolds to general base schemes and higher dimensions. It proves that certain varieties, like Xm^0, are A1-homotopic but not isomorphic as schemes over infinite perfect fields. This establishes the existence of 'exotic' motivic spheres in dimensions four and above over appropriate base schemes.