Abstract
Suppose is a hyperelliptic curve of genus defined over an algebraically closed field of characteristic . We prove that the de Rham cohomology of decomposes into pieces indexed by the branch points of the hyperelliptic cover. This allows us to compute the isomorphism class of the -torsion group scheme of the Jacobian of in terms of the Ekedahl–Oort type. The interesting feature is that depends only on some discrete invariants of , namely, on the ramification invariants associated with the branch points. We give a complete classification of the group schemes that occur as the -torsion group schemes of Jacobians of hyperelliptic -curves of arbitrary genus, showing that only relatively few of the possible group schemes actually do occur.
Citation
Arsen Elkin. Rachel Pries. "Ekedahl–Oort strata of hyperelliptic curves in characteristic 2." Algebra Number Theory 7 (3) 507 - 532, 2013. https://doi.org/10.2140/ant.2013.7.507
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