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Relative $\mathbb{A}^1$-Contractibility of Koras-Russell Prototypes and Exotic Motivic Spheres
The Koras-Russell threefolds are a certain family of smooth, affine contractible threefolds exhibiting "exotic" behavior in the algebro-geometric context. Our goal in this note is to extend its $\mathbb{A}^1$-contractibility from a field to a general base scheme. As a consequence, we also give a gen
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