动机导出傅里叶变换
A motivic derived Fourier transform
AI总结：
针对正特征域上导出Artin stacks的导出向量丛，本文构造了以Artin-Schreier动机为核的有理平展动机傅里叶变换理论，并建立了其核心基本性质，为相关研究提供了重要理论基础。
AI中文摘要：
我们针对正特征域上导出Artin stacks上的导出向量丛，构造了有理平展动机的傅里叶变换理论，将其定义为以Artin-Schreier动机为核的积分变换。建立了其基本性质：对合性、基变换、函子性、对偶性、单值性、可构造性，以及与各种自然变换的相容性。
英文摘要：
We construct a theory of Fourier transform for rational étale motives on derived vector bundles over derived Artin stacks over a field of positive characteristic, defined as the integral transform with kernel the Artin-Schreier motive. The basic properties are established: involutivity, base change, functoriality, duality, monodromicity, constructibility, and compatibilities with various natural transformations.
