The a-numbers of Jacobians of Suzuki curves
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 thi...
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| creator | Friedlander, Holley Garton, Derek Malmskog, Beth Pries, Rachel Weir, Colin |
| description | 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 \(H^0(S_m,\Omega^1)\). |
| doi_str_mv | 10.48550/arxiv.1110.6898 |
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| subjects | Isomorphism Jacobians Mathematics - Algebraic Geometry Mathematics - Number Theory Torsion |
| title | The a-numbers of Jacobians of Suzuki curves |
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