Abstract
FormâNm \in {\mathbb N}, letSmS_mbe the Suzuki curve defined overF22m+1\mathbb {F}_{2^{2m+1}}. It is well-known thatSmS_mis supersingular, but thepp-torsion group scheme of its Jacobian is not known. Theaa-number is an invariant of the isomorphism class of thepp-torsion group scheme. In this paper, we compute a closed formula for theaa-number ofSmS_musing the action of the Cartier operator onH0(Sm,Ω1)H^0(S_m,\Omega ^1).
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