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arXiv · 1207.5387

One half log discriminant and division polynomials

Robin de Jong
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Abstract

L. Szpiro and T. Tucker recently proved that under mild conditions, the valuation of the minimal discriminant of an elliptic curve with semistable reduction over a discrete valuation ring can be expressed in terms of intersections between n-torsion and 2-torsion, where n tends to infinity. The argument of Szpiro and Tucker is geometric in nature. We give a proof based on the arithmetic of division polynomials, and generalize the result to the case of hyperelliptic curves.

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Robin de Jong. 2012-07-23. One half log discriminant and division polynomials. https://arxiv.org/abs/1207.5387

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