SINGULAR CURVES OVER A FINITE FIELD AND WITH MANY POINTS
نویسندگان
چکیده
منابع مشابه
Curves over Finite Fields with Many Points: an Introduction
The number of points on a curve defined over a finite field is bounded as a function of its genus g. In this introductory article, we survey what is known about the maximum number of points on a curve of genus g defined over Fq, including an exposition of upper bounds, lower bounds, known values of this maximum, and briefly indicate some methods of constructing curves with many points, providin...
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This bound was proved for elliptic curves by Hasse in 1933. Ever since, the question of the maximum number Nq(g) of points on an irreducible curve of genus g over a finite field of cardinality q could have been investigated. But for a long time it attracted no attention and it was only after Goppa introduced geometric codes in 1980 that this question aroused systematic attention, cf. [G], [M], ...
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A general type of ray class elds of global function elds is investigated. The computation of their genera is reduced to the determination of the degrees of these extensions, which turns out to be the main diiculty. While in two special situations explicit formulas for the degrees are known, the general problem is solved algorithmically. The systematic application of the methods described yields...
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Introduction. Let C be a (smooth, projective, absolutely irreducible) curve of genus g > 2 over a number field K. Faltings [Fa1, Fa2] proved that the set C(K) of K-rational points of C is finite, as conjectured by Mordell. The proof can even yield an effective upper bound on the size #C(K) of this set (though not, in general, a provably complete list of points); but this bound depends on the ar...
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2014
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v95i2.8