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

Abstract

A 2-dimensional version of Farey dissection for function fields K = F q ( 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 ⊂ P K n − 1 $X\subset \mathbb {P}^{n-1}_{K}$ , under the assumption that q $q$ is odd and n ⩾ 9 $n\geqslant 9$ .