Abstract

Waldhausen’s algebraic $K$-theory machinery is applied to Morel–Voevodsky ${\mathbb{𝔸}}^1$-homotopy, producing an interesting ${\mathbb{𝔸}}^1$-homotopy type. Over a field $F$ of characteristic zero, its path components receive a surjective ring homomorphism from the Grothendieck ring of varieties over $F$.

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