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arXiv · 1110.6898

The a-numbers of Jacobians of Suzuki curves

Holley Friedlander·Derek Garton·Beth Malmskog·Rachel Pries·Colin Weir
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Abstract

For $m \in {\mathbb N}$, let $S_m$ be the Suzuki curve defined over ${\mathbb F}_{2^{2m+1}}$. It is well-known that $S_m$ is supersingular, but the p-torsion group scheme of its Jacobian is not known. The a-number is an invariant of the isomorphism class of the p-torsion group scheme. In this paper, we compute a closed formula for the a-number of $S_m$ using the action of the Cartier operator on $H^0(S_m,\Omega^1)$.

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Holley Friedlander, Derek Garton, Beth Malmskog, Rachel Pries, Colin Weir. 2011-10-31. The a-numbers of Jacobians of Suzuki curves. https://doi.org/10.1090/s0002-9939-2013-11581-9

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