Rational points on singular intersections of quadrics. (September 2013)

• Record Type: Journal Article
• Authors: Browning, T. D.; Munshi, R.
• Is Part Of: Compositio mathematica. Volume 149:Number 9(2013)
• Page Start: 1457
• Page End: 1494
• Publication Date: 2013-09
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X13007185
• Languages: English
• ISSNs: 0010-437X

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>Given an intersection of two quadrics <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8wbc4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$X\subset { \mathbb{P} }^{m- 1} $]]></tex-math></alternatives></inline-formula>, with <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8w94r" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$m\geq 9$]]></tex-math></alternatives></inline-formula>, the quantitative arithmetic of the set <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8wb25" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$X( \mathbb{Q} )$]]></tex-math></alternatives></inline-formula> is investigated under the assumption that the singular locus of <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8wbjw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$X$]]></tex-math></alternatives></inline-formula> consists of a pair of conjugate singular points defined over <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8wb02" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$ \mathbb{Q} (i)$]]></tex-math></alternatives></inline-formula>.</p> </abstract>