Faltings proved the arithmetic Shafarevich conjecture for (principally polarized) abelian varieties, and deduced the arithmetic Shafarevich conjecture for canonically polarized curves. It seems reasonable to suspect that analogous finiteness statements hold for canonically polarized varieties. Inspired by this philosophy, we will present an analogue of the Shafarevich conjecture for "certain" varieties of general type. Our methods rely on the theory of Néron models developed recently by Qing Liu and Jilong Tong.