Abelian tensor hierarchy and Chern-Simons actions in 4D N $$ mathcal{N} $$ = 1 conformal supergravity

We consider chern-simons actions of abelian tensor hierarchy of p-form gauge fields in four-dimensional $$ mathcal{n} $$ = 1 supergravity. using conformal superspace formalism, we solve the constraints on the field strengths of the p-form gauge superfields in the presence of the tensor hierarchy. the solutions are expressed by the prepotentials of the p-form gauge superfields. we show the internal and superconformal transformation laws of the prepotentials. the descent formalism for the chern-simons actions is exhibited.