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

Abstract

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 $X\subset {\mathbb{P}}_K^{n-1}$ , under the assumption that $q$ is odd and $n\ge 9$.

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