A motivic analogue of the K(1)-local sphere spectrum

We identify the motivic $KGL/2$-local sphere as the fiber of $\psi^3-1$ on $(2,\eta)$-completed Hermitian $K$-theory, over any base scheme containing 1/2. This is a motivic analogue of the classical $K(1)$-local sphere, and extends to a description of the $KGL/2$-localization of any motivic spectrum. Our proof relies on a novel conservativity argument that should be of broad utility in stable motivic homotopy theory. This is joint work with William Balderrama and J.D. Quigley.

There will also be a pre-talk aimed at graduate students 2:30-3:20pm in PDL C-401.