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arXiv · 2511.02733

Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-covers in characteristic $2$

Jeremy Booher·Steven R. Groen·Joe Kramer-Miller
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Abstract

In this article we study the Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-Galois covers $\pi:Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the Ekedahl-Oort type of $Y$ is completely determined by the genus of $X$ and the ramification of $\pi$. For a general base curve $X$, we prove bounds on the Ekedahl-Oort depending on the Ekedahl-Oort type of $X$ and the ramification of $\pi$. Along the way, we develop a theory of \emph{enhanced differentials of the second kind}. This theory allows us to study algebraic de Rham cohomology in any characteristic by working directly with differentials, in contrast to the standard \v{C}ech resolution.

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Jeremy Booher, Steven R. Groen, Joe Kramer-Miller. 2025-11-04. Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-covers in characteristic $2$. https://arxiv.org/abs/2511.02733

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