Varieties that are not stably rational, zero-cycles and unramified cohomology

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Abstract

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 languageEnglish (US)
Pages (from-to)459-483
Number of pages25
JournalProceedings of Symposia in Pure Mathematics
Volume97
Issue number2
DOIs
StatePublished - 2018
EventAMS Summer Institute on Algebraic Geometry, 2015 - Salt Lake City [state] UT, United States
Duration: Jul 13 2015Jul 31 2015

ASJC Scopus subject areas

  • Mathematics(all)

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