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2013 Ekedahl–Oort strata of hyperelliptic curves in characteristic 2
Arsen Elkin, Rachel Pries
Algebra Number Theory 7(3): 507-532 (2013). DOI: 10.2140/ant.2013.7.507


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 JX[2] of the Jacobian of X in terms of the Ekedahl–Oort type. The interesting feature is that JX[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 that occur as the 2-torsion group schemes of Jacobians of hyperelliptic k-curves of arbitrary genus, showing that only relatively few of the possible group schemes actually do occur.


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Arsen Elkin. Rachel Pries. "Ekedahl–Oort strata of hyperelliptic curves in characteristic 2." Algebra Number Theory 7 (3) 507 - 532, 2013.


Received: 7 July 2010; Revised: 11 April 2012; Accepted: 16 April 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1282.11065
MathSciNet: MR3095219
Digital Object Identifier: 10.2140/ant.2013.7.507

Primary: 11G20
Secondary: 11G10, 14F40, 14H40, 14K15, 14L15

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.7 • No. 3 • 2013
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