Nicolas Addington (Oregon) - Birational invariants from higher algebraic K-theory?

Many have tried to adapt Clemens and Griffiths's approach to irrationality of cubic threefolds to higher dimensions, using different invariants in place of H^3(X,Z): the transcendental part of H^4, derived categories, quantum cohomology... I will report on my attempt to use higher algebraic K-theory, which turns out to be strictly weaker than what Voisin and Colliot-Thélène have already gotten from Bloch-Ogus theory, but (I think) in an interesting way. For a positive result, I can show that the higher K-theory of Kuznetsov's K3 category for a cubic or Gushel-Mukai 4-fold looks the same as that of an honest K3 surface.