The weak local Arthur packets conjecture

Let $\mathrm{G}$ be a connected reductive group and let $G=\mathrm{G}(F)$. Assume that a local Arthur packets theory exists for $G$ as conjectured by Arthur. Let $\psi$ be a basic local Arthur parameter of $G$, and let $\lambda$ be the associated real infinitesimal parameter. Define

$$\Pi_{\psi}^{\textrm{Weak}}:=\{\pi\in\Pi(G)_{\lambda}\mid \overline{\mathfrak{n}}^{m}(\pi)\leq d_{BV}({\mathcal O}_{\psi}^{A})\}.$$

The weak local Arthur packets conjecture. The set $\Pi_{\psi}^{\textrm{Weak}}$ is a union of local Arthur packets.

This conjecture proposes that the geometric wavefront-set bound defined using Barbasch–Vogan duality decomposes into genuine local Arthur packets. The paper proves it for split classical groups when the residue-field characteristic is sufficiently large.