NDLI: The Hardy–Littlewood conjecture and rational points

Content Provider	Scilit
Author	Harpaz, Yonatan Skorobogatov, Alexei N. Wittenberg, Olivier
Copyright Year	2014
Description	Journal: Compositio Mathematica Schinzel’s Hypothesis (H) was used by Colliot-Thélène and Sansuc, and later by Serre, Swinnerton-Dyer and others, to prove that the Brauer–Manin obstruction controls the Hasse principle and weak approximation on pencils of conics and similar varieties. We show that when the ground field is $\mathbb{Q}$ and the degenerate geometric fibres of the pencil are all defined over $\mathbb{Q}$, one can use this method to obtain unconditional results by replacing Hypothesis (H) with the finite complexity case of the generalised Hardy–Littlewood conjecture recently established by Green, Tao and Ziegler.
Ending Page	2111
Starting Page	2095
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x14007568
Journal	Compositio Mathematica
Issue Number	12
Volume Number	150
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2014-09-10
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics Littlewood Conjecture
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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The Hardy–Littlewood conjecture and rational points