On the order of points on curves over finite fields
نویسنده
چکیده
We discuss the problem of constructing elements of multiplicative high order in finite fields of large degree over their prime field. We prove that for points on a plane curve, one of the coordinates has to have high order. We also discuss a conjecture of Poonen for subvarieties of semiabelian varieties for which our result is a weak special case. Finally, we look at some special cases where we obtain sharper bounds.
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