Original version
International Mathematics Research Notices (IMRN). 2023, 1-34, DOI: https://doi.org/10.1093/imrn/rnad094
Abstract
We analyze the question of which motivic homotopy types admit smooth schemes as representatives. We show that given a pointed smooth affine scheme X and an embedding into affine space, the affine deformation space of the embedding gives a model for the P1 suspension of X; we also analyze a host of variations on this observation. Our approach yields many examples of A1-(n−1)-connected smooth affine 2n-folds and strictly quasi-affine A1-contractible smooth schemes.