Extended conformal supergravity

We present the complete structure of extended conformal supergravity for N ≤ 4. The relation with the graded algebra SU(2, 2|N) and with the multiplet of currents is discussed. The N = 4 superconformal theory has a formulation with local SU(4) × U(1) and rigid SU(1, 1) invariance. We give the linearized invariant actions for all N. For N = 2 we exhibit the complete non-linear lagrangian