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

A Kloosterman refinement for function fields $K={\mathbb{F}}_q(t)$ is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics $X\subset $\mathbb{P}$^{n-1}_{K}$,undertheassumptionthat$q$isoddand$n\geq 9$.