On the Hasse principle for complete intersections

Abstract

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

68 pages, 3 figures