The Hasse principle for random Fano hypersurfaces

T.D. Browning, P.L. Boudec, W. Sawin, ArXiv (n.d.).

Preprint | Submitted | English
Author
Browning, Timothy DIST Austria; Boudec, Pierre Le; Sawin, Will
Department
Abstract
It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.
Publishing Year
Date Published
2020-06-03
Journal Title
arXiv
Article Number
2006.02356
IST-REx-ID

Cite this

Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. arXiv.
Browning, T. D., Boudec, P. L., & Sawin, W. (n.d.). The Hasse principle for random Fano hypersurfaces. ArXiv.
Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” ArXiv, n.d.
T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” arXiv. .
Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. arXiv.
Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” ArXiv, 2006.02356.
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