Integral points on plane curves and Plane Jacobian Conjecture over number fields

2017/09/12 by Van Chau, Nguyen
#11D72 (secondary) #14R15 (primary) #14R25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.03664

Abstract

Let K be a number field and O_K the ring of integers of K. In the spirit of Siegel's theorem on integral points on affine algebraic curves, the plane Jacobian conjecture over K is equivalent to the following statement: if P,Q∈ O_K[x,y] and P_xQ_y-P_yQ_x≡ 1, then the curve P=0 has more than one integral point.

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• Jacobian conjecture as a problem on integral points on affine curves
• The plane Jacobian conjecture for rational curves
• Integral curves and Jacobian Conjecture
• Jacobian Conjecture in two dimension
• Siegel's theorem on integral points and the Jacobian conjecture over the\n rational field