Alena Pirutka
Published 2016-03-30Version 1
This is a survey of recent examples of varieties that are not stably rational. We review the specialization method based on properties of the Chow group of zero-cycles used in these examples and explain the point of view of unramified cohomology for the construction of nontrivial stable invariants of the special fiber. In particular, we find an explicit formula for the Brauer group of fourfolds fibered in quadrics of dimension two over a rational surface.
Compatibility of weak approximation for zero-cycles on products of varieties
Tilting chains of negative curves on rational surfaces
Green's Conjecture for curves on rational surfaces with an anticanonical pencil
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