Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ekedahl-Oort strata of hyperelliptic curves in characteristic 2   Suppose $X$ is a hyperelliptic curve of genus $g$ defined over an
algebraically closed field $k$ of characteristic $p=2$. We prove that the de
Rham cohomology of $X$ decomposes into pieces indexed by the branch points of
the hyperelliptic cover. This allows us to compute the isomorphism class of the
$2$-torsion group scheme $J_X[2]$ of the Jacobian of $X$ in terms of the
Ekedahl-Oort type. The interesting feature is that $J_X[2]$ depends only on
some discrete invariants of $X$, namely, on the ramification invariants
associated with the branch points. We give a complete classification of the
group schemes which occur as the $2$-torsion group schemes of Jacobians of
hyperelliptic $k$-curves of arbitrary genus.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int