Arthur packets for

In this article we propose a geometric description of Arthur packets for $p$-adic groups using vanishing cycles perverse sheaves. Our approach is inspired by the 1992 book Adams, Barbasch and Vogan on Langlands classification admissible representations real follows direction indicated in his 1993 paper correspondence. Using cycles, introduce study functor from category equivariant sheaves moduli space certain parameters to local systems regular part conormal bundle variety. establish main properties show that it plays role microlocalization work Vogan. We use define ABV-packets pure rational forms transfer coefficients appear Arthur's result endoscopic representations. This includes conjectures modelled Vogan's work, especially prediction are groups. gather evidence these verifying them numerous examples.