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arXiv · 2512.04300

Logarithmic de Rham Stacks and Non-Abelian Hodge Theory

Michael Barz
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Abstract

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.

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Michael Barz. 2025-12-03. Logarithmic de Rham Stacks and Non-Abelian Hodge Theory. https://arxiv.org/abs/2512.04300

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