Rational points on quartic hypersurfaces

✍ Scribed by Browning, T. D.; Heath-Brown, D. R.

• Book ID: 121410349
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2009
• Tongue: English
• Weight: 432 KB
• Volume: 2009
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2009.026

✦ Synopsis

Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over Q. We show that X ðQÞ is non-empty provided that X ðRÞ is non-empty and X has p-adic points for every prime p.

Browning and Heath-Brown, Rational points on quartic hypersurfaces