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math.NT2012
A height inequality for rational points on elliptic curves implied by the abc-conjecture
Ulf Kühn, J. Steffen Müller
In this short note we show that the uniform abc-conjecture over number fields puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we us…
math.NT2012★ 2 cited
Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces
Ulf Kühn, Jan Steffen Müller
We give an explicitly computable lower bound for the arithmetic self-intersection number of the dualizing sheaf on a large class of arithmetic surfaces. If some technical condition…