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