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Unramified Brauer groups of conic bundle threefolds in characteristic two
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 5, October 2021
- pp. 1601-1631
- 10.1353/ajm.2021.0040
- Article
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Abstract:
We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic $2$. The formula depends on the arrangement and residue double covers of the discriminant components, the latter being governed by Artin-Schreier theory (instead of Kummer theory in characteristic not $2$). We use this to give new examples of threefold conic bundles defined over $\Bbb{Z}$ that are not stably rational over $\Bbb{C}$.