George H. Hitching
Published 2007-06-29Version 1
Let K be a field of characteristic different from 2 and C an elliptic curve over K given by a Weierstrass equation. To divide an element of the group C by 2, one must solve a certain quartic equation. We characterise the quartics arising from this procedure and find how far the quartic determines the curve and the point. We find the quartics coming from 2-division of 2- and 3-torsion points, and generalise this correspondence to singular plane cubics. We use these results to study the question of which degree 4 maps of curves can be realised as duplication of a multisection on an elliptic surface.
P-torsion monodromy representations of elliptic curves over geometric function fields
On the structure of elliptic curves over finite extensions of $\mathbb{Q}_p$ with additive reduction
Hodge theory and the Mordell-Weil rank of elliptic curves over extensions of function fields
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