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

Alena Pirutka

doi:10.1090/pspum/097.2/01713

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

Alena Pirutka

Mathematics

Research output: Contribution to journal › Conference article › peer-review

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 language	English (US)
Pages (from-to)	459-483
Number of pages	25
Journal	Proceedings of Symposia in Pure Mathematics
Volume	97
Issue number	2
DOIs	https://doi.org/10.1090/pspum/097.2/01713
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

General Mathematics

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10.1090/pspum/097.2/01713

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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.",

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

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