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Rational points on singular intersections of quadrics

Part of: Diophantine equations Arithmetic problems. Diophantine geometry Forms and linear algebraic groups Additive number theory; partitions Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  20 June 2013

T. D. Browning  and
R. Munshi
T. D. Browning
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK email [email protected]
R. Munshi
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400005, India email [email protected]
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Abstract

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Given an intersection of two quadrics $X\subset { \mathbb{P} }^{m- 1} $, with $m\geq 9$, the quantitative arithmetic of the set $X( \mathbb{Q} )$ is investigated under the assumption that the singular locus of $X$ consists of a pair of conjugate singular points defined over $ \mathbb{Q} (i)$.

Keywords

Hardy–Littlewood circle methodpairs of quadratic formsrational points

MSC classification

Secondary: 11D72: Equations in many variables 11E12: Quadratic forms over global rings and fields 11P55: Applications of the Hardy-Littlewood method 14G25: Global ground fields 14J20: Arithmetic ground fields
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 9 , September 2013 , pp. 1457 - 1494
Copyright
© The Author(s) 2013 

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