Varieties that are not stably rational, zero-cycles and unramified cohomology
Algebraic Geometry
2016-08-29 v2 Number Theory
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 two over a rational surface.
Keywords
Cite
@article{arxiv.1603.09261,
title = {Varieties that are not stably rational, zero-cycles and unramified cohomology},
author = {Alena Pirutka},
journal= {arXiv preprint arXiv:1603.09261},
year = {2016}
}
Comments
24 pages, revised version