Base Change Fundamental Lemma for Central Elements in Depth-zero Hecke Algebras over Local Function Fields

Abstract

Let $G$ be an unramified group over a local function field of characteristic $p>0$. This article introduces an abstract norm map between the twisted conjugacy classes and conjugacy classes of $G$ in the positive characteristics setting, applies the process of stabilization of (twisted) trace formula and proves the corresponding base change fundamental lemma for regular semisimple elements.