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On the Hasse principle for complete intersections
Part of
Matthew Northey, Pankaj Vishe
Journal:

Compositio Mathematica / Volume 160 / Issue 4 / April 2024

Published online by Cambridge University Press:

05 March 2024, pp. 771-835

Print publication:

April 2024
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We prove the Hasse principle for a smooth projective variety $X\subset \mathbb {P}^{n-1}_\mathbb {Q}$ defined by a system of two cubic forms $F,G$ as long as $n\geq 39$. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over $\mathbb {Q}$.