It is is important not to say things like 'Jesus died and came back to life' -- as if he were merely resuscitated to a prolonged spell of earthly life before dying in the end. Jesus did not die and 'come back'. Jesus died and went forward--forward into the new resurrection life of the age to come. He is the firstfruits of the new creation. So his resurrection is the guarantee of ours, and of the whole new creation life we will enjoy with him, when he 'will transform our lowly bodies so that they will be like his glorious body' (Phil. 3:21).
And of course it is the risen Christ who has sent his Spirit, as he promised, whose primary work... is to apply God's salvation in our hearts, bearing witness to our sonship, bearing fruit in our lives, strengthening and comforting us in our witness to Christ.