Effective Hasse principle for the intersection of two quadrics

Abstract

We consider a smooth system of two homogeneous quadratic equations over $\mathbb{Q}$ in $n\geqslant 13$ variables. In this case, the Hasse principle is known to hold, thanks to the work of Mordell in 1959. The only local obstruction is over $\mathbb{R}$ . In this paper, we give an explicit algorithm to decide whether a nonzero rational solution exists and, if so, compute one.

Locations

• LMS Journal of Computation and Mathematics - View - PDF
• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
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