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arXiv · 2112.08241

Geometric models for algebraic suspensions

Aravind Asok·Adrien Dubouloz·Paul Arne Østvær
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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 ${\mathbb P}^1$ suspension of $X$; we also analyze a host of variations on this observation. Our approach yields many examples of ${\mathbb A}^1$-$(n-1)$-connected smooth affine $2n$-folds and strictly quasi-affine ${\mathbb A}^1$-contractible smooth schemes.

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BibTeXRIS

Aravind Asok, Adrien Dubouloz, Paul Arne Østvær. 2021-12-15. Geometric models for algebraic suspensions. https://arxiv.org/abs/2112.08241

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