|Location:||MSRI: Simons Auditorium|
In previous joint work with Hoyois, Khan, Sosnilo and Yakerson we obtained (up to group completion) a geometric description of the $0$-th space of the motivic sphere spectrum in terms of a certain torsor over an open subscheme of the Hilbert scheme of points in infinite dimensional affine space. The base scheme is smooth and turns out to describe the $0$-th space of Voevodsky's algebraic cobordism spectrum. The problem of describing the $n$-th space is currently in progress and the description involves the moduli of derived schemes of virtual dimension $-n$.
In this talk, I will discuss these results and some of its corollaries, especially those concerning generation results on Chow groups of smooth complex varieties. A gentle introduction to motivic homotopy theory and previous work will be included.
All this is joint with Hoyois, Khan, Sosnilo and Yakerson.No Notes/Supplements Uploaded No Video Files Uploaded