Zeros of Pairs of Quadratic Forms

D. R. Heath-Brown

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arXiv · 1304.3894

Zeros of Pairs of Quadratic Forms

D. R. Heath-Brown

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Abstract

We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in 8 variables. The argument develops work of Colliot-Thelene, Sansuc and Swinnerton-Dyer, and centres on a purely local problem about forms which split off 3 hyperbolic planes.

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D. R. Heath-Brown. 2013-04-14. Zeros of Pairs of Quadratic Forms. https://arxiv.org/abs/1304.3894

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