A description of the motive of $\mathrm{Hilb}(\mathbb{A}^\infty)$

Abstract: The Hilbert scheme of points in infinite affine space is a very complicated algebro-geometric object, whose local structure is extremely rich and hard to describe. In this talk I will show that nevertheless its motive is pure Tate and in fact it coincides with the motive of the Grassmannian. This will allow us to give a simple conceptual description of the motivic algebraic K-theory spectrum. This is joint work with Marc Hoyois, Joachim Jelisiejew, Burt Totaro and Maria Yakerson.

algebraic geometryalgebraic topology

Audience: researchers in the topic

MoVid-20

Series comments: Description: A one day conference on motivic homotopy theory

In order to register for the conference, please send an email to Denis Nardin (denis DOT nardin AT ur DOT de) with subject "MoVid-20"