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 ${\mathrm{GL}}_n$ over local function fields of characteristic $p>0$, and for ${\mathrm{Sp}}_{2n}$, split ${\mathrm{SO}}_{2n}$, ${\mathrm{SO}}_{2n+1}$, and ${\mathrm{GSp}}_4$ over local function fields of characteristic $p>2$.