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Edges of the Quillen-Lichtenbaum range and birational geometry

Elden Elmanto, University of Toronto
Friday, August 25, 2023 - 3:30pm to 4:30pm
PDL C-401
Elden Elmanto

The Quillen-Lichtenbaum conjecture, now proved by Rost and Voevodsky, in particular asserts that the algebraic K-theory of a smooth C-scheme is equivalent to its topological K-theory 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 dg-categories and is thus a Morita invariant. I will explain some examples and computations of this birational invariant and its connections with the so-called "cofiber of tau" in motivic homotopy theory.

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