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arXiv · 1903.08015

The Clemens-Griffiths method over non-closed fields

Olivier Benoist·Olivier Wittenberg
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Abstract

We use the Clemens-Griffiths method to construct smooth projective threefolds, over any field $k$ admitting a separable quadratic extension, that are $k$-unirational and $\bar{k}$-rational but not $k$-rational. When $k=\mathbb{R}$, we can moreover ensure that their real locus is diffeomorphic to the real locus of a smooth projective $\mathbb{R}$-rational variety and that all their unramified cohomology groups are trivial.

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Olivier Benoist, Olivier Wittenberg. 2019-03-19. The Clemens-Griffiths method over non-closed fields. https://doi.org/10.14231/ag-2020-025

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