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 2 over a rational surface.
|Original language||English (US)|
|Number of pages||25|
|Journal||Proceedings of Symposia in Pure Mathematics|
|State||Published - 2018|
|Event||AMS Summer Institute on Algebraic Geometry, 2015 - Salt Lake City [state] UT, United States|
Duration: Jul 13 2015 → Jul 31 2015
ASJC Scopus subject areas