# Algebraic Geometry Seminar

#### On the higher K-theory of some complex varieties

**Speaker:**
Nicolas Addington, University of Oregon

**Location:**
Warren Weaver Hall 512

**Date:**
Tuesday, April 16, 2024, 3:30 p.m.

**Synopsis:**

The algebraic K-theory of a smooth complex variety is very different from

topological K-theory of the underlying manifold, but if we take Z/m

coefficients, they become more closely related, and in fact isomorphic in

high degrees. The point at which they become isomorphic is an interesting

invariant of the variety, which I'll relate to more classical invariants

and to birational geometry. Then I'll use it to prove the integral Hodge

conjecture for some complex 4-folds, and to describe the higher K-theory

of the "Kuznetsov component" of derived categories of some hypersurfaces.

This is joint work with Elden Elmanto.