Curves with many points
نویسنده
چکیده
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 arithmetic of C. This suggests the question of how #C(K) behaves as C varies. Following [CHM1, CHM2], given g > 2 and K we define: B(g,K) = maxC#C(K), (1)
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