MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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)?

share|cite|improve this question

See . "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.

share|cite|improve this answer
The article you mentioned has a definition of supersingular but not of ordinary, right? – expmat May 11 '12 at 18:31
My answer has a definition of ordinary but not of supersingular, on the other hand. – Charles Matthews May 11 '12 at 19:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.