Peel the asparagus and cook for 10 minutes with a little salt.Let stand off the heat for 20 minutes.Meanwhile, scrub the lime and grate the green zest off,squeeze half a lime, peel and chop garlic. In thefood processor basil, garlic and 1 tablespoon lime juicemix with the olive oil to a smooth marinade. Lime zeststir in, add salt and pepper to taste. Marinadetransfer to a low baking dish.Drain the asparagus and place in the marinade and thespoon marinade over it. Leave asparagus in the marinadecool and turn occasionally.
Rinse shrimp in a sieve and drain.
Tear arugula into pieces and divide among 4 plates.Asparagus from the marinade with the heads to one side on thelay plates. Distribute shrimp on top and a littledrizzle marinade over.