Hesse Pencils and 3-Torsion Structures

Ane S. I. Anema, Jaap Top, Anne Tuijp

Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands

Abstract: This paper intends to focus on the universal property of this Hesse pencil and of its twists. The main goal is to do this as explicit and elementary as possible, and moreover to do it in such a way that it works in every characteristic different from three.

Keywords: Hesse pencil; Galois representation; torsion points; elliptic curves.

MSC: 14D10; 14G99

Received: May 8, 2018; in final form September 18, 2018; Published online September 21, 2018

Language: English

DOI: 10.3842/SIGMA.2018.102

Bibliographic databases:

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ArXiv: 1708.09745