Let C and C’ be two smooth projective curves over an algebraic closure of the rational numbers . We call C lies over C’ if there is an unramified cover of C which admits a surjective map to C’ and call C and C’ are equilvalent if C lies over C’ and C’ also lies over C. This relation between curves was initiated by Bogomolov and Tschinkel. They have also conjectured that all hyperbolic curves are equilvalent. Based on the method of contraction of algebraic points via projective line and some elliptic curves, in this talk we will discuss several results about this problem.

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