On the Hasse principle for complete intersections

2021/12/21 by Northey, Matthew, Vishe, Pankaj
#11D72 (Primary) 11P55 #14G05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.11303

Abstract

We prove the Hasse principle for a smooth projective variety X⊂ \PP^n-1_\Q 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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