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Hesse pencil in characteristic two

Tuijp, A. (2015) Hesse pencil in characteristic two. Bachelor's Thesis, Mathematics.

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In this paper we look at flex points on elliptic curves and to what extend they characterize the curve itself. In characteristic different from two and three, there exists a certain theorem about this by A. Anema. We will show that this theorem is also true in characteristic two. First, we give a short introduction to elliptic curves, the three-torsion group and the Weil-pairing. Then, given an elliptic curve in characteristic two, we define a curve that is in some way analogous to the Hessian in other characteristics: it intersects the elliptic curve only at its flex points. We use this alternative Hessian curve to define a Hesse pencil in characteristic two. Finally, we prove the only remaining proposition in Anema's proof for which an alternative proof is needed in characteristic two.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:06
Last Modified: 15 Feb 2018 08:06

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