In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure L of a finite field with coefficients in a global function field over this finite field. It is semi-simple, non-neutral Tannakian and possesses all the expected fiber functors. This category generalizes the previous construction due to Anderson and is more relevant for applications to the theory of G-Shtukas, such as formulating the analog of the Langlands-Rapoport conjecture over function fields. We further develop the analogy with the category of motives over L with coefficients in $\mathbb{Q}$ for which the existence of the expected fiber functors depends on famous unproven conjectures.

在本文中，我们介绍并研究了函数域算法中的一个动机范畴，即有限域的代数闭包L上的动机范畴，该有限域上的全局函数域的系数。它是半简单的、非中性的 Tannakian，并拥有所有预期的纤维函子。此类别概括了由于安德森的先前构造，并且与G- Shtukas理论的应用更相关，例如在函数场上制定朗兰兹-拉波波特猜想的类比。我们进一步发展了与L上的动机类别的类比，系数为$\mathbb{问}$ 预期纤维函子的存在取决于著名的未经证实的猜想。