I’ve posted a new paper here (and on the arXiv). It uses the Chow group of algebraic cycles to study a fundamental question in algebraic geometry: which hypersurfaces are stably rational varieties. The result is that for all d at least about 2n/3, a very general complex hypersurface of degree d and dimension n is not stably rational. This is a wide generalization of Colliot-Thélène and Pirutka’s theorem that very general quartic 3-folds are not stably rational. In a vague sense it uses the same machine as last week’s paper.
Drawing by Edward Gorey via Goreyana