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arXiv · 1710.08544

The de Rham cohomology of the Suzuki curves

Beth Malmskog·Rachel Pries·Colin Weir
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Abstract

For a natural number $m$, let $\mathcal{S}_m/\mathbb{F}_2$ be the $m$th Suzuki curve. We study the mod $2$ Dieudonn\'{e} module of $\mathcal{S}_m$, which gives the equivalent information as the Ekedahl-Oort type or the structure of the $2$-torsion group scheme of its Jacobian. We accomplish this by studying the de Rham cohomology of $\mathcal{S}_m$. For all $m$, we determine the structure of the de Rham cohomology as a $2$-modular representation of the $m$th Suzuki group and the structure of a submodule of the mod $2$ Dieudonn\'{e} module. For $m=1$ and $2$, we determine the complete structure of the mod $2$ Dieudonn\'{e} module.

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Beth Malmskog, Rachel Pries, Colin Weir. 2017-10-23. The de Rham cohomology of the Suzuki curves. https://arxiv.org/abs/1710.08544

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