The Clemens-Griffiths method over non-closed fields
Benoist, Olivier ; Wittenberg, Olivier
arXiv, Tome 2019 (2019) no. 0, / Harvested from
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 $\overline{k}$-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.
Publié le : 2019-03-19
Classification:  Mathematics - Algebraic Geometry,  14M20, 14E08, 14K30 
@article{1903.08015,
     author = {Benoist, Olivier and Wittenberg, Olivier},
     title = {The Clemens-Griffiths method over non-closed fields},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1903.08015}
}

Benoist, Olivier; Wittenberg, Olivier. The Clemens-Griffiths method over non-closed fields. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1903.08015/