Is there a standard meaning for ordinary and supersingular Abelian varieties over finite fields? If so, where can I find it (together with basic properties about them)?


See http://en.wikipedia.org/wiki/Hasse-Witt_matrix#Abelian_varieties_and_their_p-rank . "Ordinary" is always defined by p-rank equal to the dimension (the maximum possible). The article gives one definition of "supersingular", but that usage may not be universal.

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  • $\begingroup$ The article you mentioned has a definition of supersingular but not of ordinary, right? $\endgroup$ – expmat May 11 '12 at 18:31
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    $\begingroup$ My answer has a definition of ordinary but not of supersingular, on the other hand. $\endgroup$ – Charles Matthews May 11 '12 at 19:07

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