Abstract
We investigate a family of Châtelet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fails the Hasse principle, by building on previous work of De La Bretèche and Browning.
Original language | English |
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Pages (from-to) | 1237-1249 |
Number of pages | 13 |
Journal | International Journal of Number Theory |
Volume | 15 |
Issue number | 6 |
Early online date | 13 Feb 2019 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
Keywords
- Brauer-Manin obstruction
- Châtelet surfaces
- Hasse principle