Abstract: In 1989, Arthur proposed a definition of local Arthur packets which arose from global considerations. A couple years later, ABV-packets were defined by purely local methods for connected reductive real groups and Vogan conjectured that they generalize local Arthur packets. More recently, Cunningham et al. defined ABV-packets for p-adic groups which also conjecturally generalize local Arthur packets. In this talk, we consider some intersection problems for ABV-packets of p-adic groups motivated by local Arthur packets.