  We prove $\ell^{p}L^{p}$ decoupling inequalities for a class of moment
manifolds. These inequalities imply optimal mean value estimates for
multidimensional Weyl sums of the kind considered by Arkhipov, Chubarikov, and
Karatsuba and by Parsell. In our proofs we take a new point of view on the
Bourgain--Demeter--Guth induction on scales argument. This point of view
substantially simplifies even the proof of $\ell^{2}L^{p}$ decoupling for the
moment curve.
