Rational points on complete intersections over Fq(t)${\mathbb {F}}_q(t)$

Abstract

A 2‐dimensional version of Farey dissection for function fields K=Fq(t)$K=\mathbb {F}_q(t)$ is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics X⊂PKn−1$X\subset \mathbb {P}^{n-1}_{K}$ , under the assumption that q$q$ is odd and n⩾9$n\geqslant 9$ .