EVENT DETAILS AND ABSTRACT

Title: A failed attempt at irrationality via algebraic K-theory
Speaker: Nicolas Addington
Speaker Info: University of Oregon
Brief Description:
Special Note:
Abstract:

The Quillen-Lichtenbaum conjecture, proved by Voevodsky, states that for smooth complex n-folds, the map from algebraic to topological K-theory with finite coefficients is an isomorphism in degree n-1 and higher, and injective in degree n-2. From this one can construct a birational invariant, and surprisingly it is somewhat computable. But it turns out to vanish for many classes of varieties where the rationality problem is hard, including cubic fourfolds; the proof repackages cycle-theoretic results of Voisin, M. Shen, and others in an interesting way. Or to state a positive result, the algebraic K-theory of Kuznetsov's K3 category behaves like that of an honest surface. This is work in progress with Elden Elmanto.