Elden Elmanto, University of Toronto

PDL C401
The QuillenLichtenbaum conjecture, now proved by Rost and Voevodsky, in particular asserts that the algebraic Ktheory of a smooth Cscheme is equivalent to its topological Ktheory in a range. In joint work with Nick Addington, we turned this number into a birational invariant which has the advantage that it is defined for dgcategories and is thus a Morita invariant. I will explain some examples and computations of this birational invariant and its connections with the socalled "cofiber of tau" in motivic homotopy theory.