The effective action of warped M-theory reductions with higher derivative terms - Part I

M-theory accessed via eleven-dimensional supergravity admits globally consistent warped solutions with eight-dimensional compact spaces if background fluxes and higher derivative terms are considered. The internal background is conformally K\"ahler with vanishing first Chern class. We perturb these solutions including a finite number of K\"ahler deformations of the metric and vector deformations of the M-theory three-form. Special emphasis is given to the field-dependence of the warp-factor and the higher-derivative terms. We show that the three-dimensional two-derivative effective action takes a surprisingly simple form in terms of a single higher-curvature building block due to numerous non-trivial cancellations. Both the ansatz and the effective action admit a moduli dependent scaling symmetry of the internal metric. Furthermore, we find that the required departure from Ricci-flatness and harmonicity of the zero-mode eigenforms does not alter the effective theory.