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Pré-Publication, Document De Travail Année : 2021

Geometric models for algebraic suspensions

Aravind Asok
  • Fonction : Auteur
Paul Arne Østvær
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03482860 , version 1 (16-12-2021)

Identifiants

Citer

Adrien Dubouloz, Aravind Asok, Paul Arne Østvær. Geometric models for algebraic suspensions. 2021. ⟨hal-03482860⟩
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