Logarithmic de Rham Stacks and Non-Abelian Hodge Theory

In this article, we introduce the logarithmic de Rham stack of a pair (X, D), for a smooth variety X over a field k of positive characteristic p, and D a strict normal crossings divisor on X. Using this stack, we prove a new version of logarithmic Cartier descent, and a new logarithmic non-abelian Hodge theorem for curves, both stated using a certain logarithmic Frobenius twist. Our logarithmic non-abelian Hodge theorem implies an earlier logarithmic non-abelian Hodge theorem of de Cataldo-Zhang.