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We prove the Hasse principle for a smooth projective variety X⊂ Pⁿ⁻¹Q defined by a system of two cubic forms $F,G$ as long as n≥ 39 . The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over Q .
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Northey et al. (2024) studied this question.
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