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)?
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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.
answered May 11, 2012 at 18:23
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$\begingroup$ The article you mentioned has a definition of supersingular but not of ordinary, right? $\endgroup$– expmatMay 11, 2012 at 18:31
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5$\begingroup$ My answer has a definition of ordinary but not of supersingular, on the other hand. $\endgroup$ May 11, 2012 at 19:07