Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 3 (2013), 507-532.
Ekedahl–Oort strata of hyperelliptic curves in characteristic 2
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.
Algebra Number Theory, Volume 7, Number 3 (2013), 507-532.
Received: 7 July 2010
Revised: 11 April 2012
Accepted: 16 April 2012
First available in Project Euclid: 20 December 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G20: Curves over finite and local fields [See also 14H25]
Secondary: 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx] 14L15: Group schemes 14H40: Jacobians, Prym varieties [See also 32G20] 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]
Elkin, Arsen; Pries, Rachel. Ekedahl–Oort strata of hyperelliptic curves in characteristic 2. Algebra Number Theory 7 (2013), no. 3, 507--532. doi:10.2140/ant.2013.7.507. https://projecteuclid.org/euclid.ant/1513729964