Abstract
AbstractIn the first half of this paper, we investigate a superspecialty criterion with respect to $\lambda$ for the curve which is a generalization of a theorem for an elliptic curve by Max Deuring (1941). In the last half, we study a criterion with respect to the characteristic $p>0$ of the ground field such that the Picard curve is superspecial or ordinary. In the final section (appendix), we consider another viewpoint of the first result by using a fact that the first curve has a completely decomposable Jacobian.
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