## EVENT DETAILS AND ABSTRACT

**Algebraic Geometry Seminar**
**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.

**Date:** Wednesday, March 08, 2023

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Yuchen Liu

**Contact email:** yuchenl@northwestern.edu

**Contact Phone:**

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