Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for \({\text {GL}}_n\) over local function fields. This generalizes a theorem of Ngô, who proved the base change fundamental lemma for spherical Hecke algebras for \({\text {GL}}_n\) over local function fields, and extends to positive characteristic (for \({\text {GL}}_n\)) a fundamental lemma originally introduced and proved by Haines for p-adic local fields.

中文翻译：

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附近的顺甲shtukas周期，以及碱基变化的基本引理

使用Langlands–Kottwitz范式，我们计算了由Hecke算符组成的Frobenius迹线，它在附近模数，顺斜减少的地方，某些模数堆叠的t轮上的邻近轮的同调上。根据Ngô的论点，然后我们使用它给出几何函数证明，证明在局部函数域上\（{\ text {GL}} _ n \）的准horkee代数的基本变化基本引理。这推广了Ngô的一个定理，他证明了局部函数场上\（{\ text {GL}} _ n \）的球面Hecke代数的基本变化基本引理，并扩展到正特征（对于\（{\ text {GL }} _ n \））最初由Haines引入并证明用于p -adic局部场的基本引理。