The formal degree conjecture for groups over local function fields

Abstract

In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan correspondence. Consequently, we establish the formal degree conjecture for $\operatorname{GL}_n$ over local function fields of characteristic $p > 0$, and for $\operatorname{Sp}_{2n}$, split $\operatorname{SO}_{2n}$, $\operatorname{SO}_{2n+1}$, and $\operatorname{GSp}_4$ over local function fields of characteristic $p > 2$.