# The Hilbert scheme of infinite affine space and algebraic K-theory

15 Sep 2020 Hoyois Marc Jelisiejew Joachim Nardin Denis Totaro Burt Yakerson Maria

We study the Hilbert scheme $\mathrm{Hilb}_d(\mathbb{A}^\infty)$ from an $\mathbb{A}^1$-homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilbert scheme $\mathrm{Hilb}_d(\mathbb{A}^\infty)$ is $\mathbb{A}^1$-equivalent to the Grassmannian of $(d-1)$-planes in $\mathbb{A}^\infty$... (read more)

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# Categories

• ALGEBRAIC GEOMETRY
• ALGEBRAIC TOPOLOGY
• K-THEORY AND HOMOLOGY