THE RANK OF THE CARTIER OPERATOR ON CERTAIN Fq2-MAXIMAL FUNCTION FIELDS

Missouri Journal of Mathematical Sciences（2022）

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摘要

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 Xq +1 + Yq +1 + Zq +1 = 0 with q = ps over the finite field Fq2 , using the action of the Cartier operator on H0(X , ohm 1).

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关键词

a-number, Cartier operator, Supersingular Curves, Max-imal Curves

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