Algebraic Geometry Seminar

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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.