6533b82afe1ef96bd128c265

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Geometric models for algebraic suspensions

A AsokA DuboulozP A ØStvær

subject

Mathematics - Algebraic GeometryMathematics - Geometric Topology14F42 14D06 55P40General MathematicsMathematics - K-Theory and HomologyFOS: Mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Topology (math.AT)Geometric Topology (math.GT)K-Theory and Homology (math.KT)[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic TopologyAlgebraic Geometry (math.AG)

description

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.

yearjournalcountryeditionlanguage
2021-12-16
https://hal.science/hal-03482860