A characterization of maximal and minimal Fermat curves
نویسندگان
چکیده
منابع مشابه
A note on superspecial and maximal curves
In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.
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where C(Fq) denotes the set of Fq-rational points of the curve C. Here we will be interested in maximal(resp. minimal) curves over Fq2 , that is, we will consider curves C attaining Hasse-Weil’s upper (resp. lower) bound: #C(Fq2) = q + 1 + 2gq (resp. q + 1− 2gq). Here we are interested to consider the hyperelliptic curve C given by the equation y = x + 1 over Fq2 . We are going to determine whe...
متن کاملa note on superspecial and maximal curves
in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.
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The Hasse principle is said to hold for a class of varieties over a number field K if for any variety X in the class, the set of rational points X(K) is non-empty whenever the set of adelic points X(AK) is non-empty. Manin [Man] observed that the failure of the Hasse principle can often be explained in terms of the Brauer group of X, Br(X). The product rule implies that X(K) must be contained i...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2010
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2009.10.001