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arXiv · 0810.3147

Torsion bounds for elliptic curves and Drinfeld modules

Florian Breuer
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Abstract

We derive asymptotically optimal upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L:K]. Our main tool is the adelic openness of the image of Galois representations attached to elliptic curves and Drinfeld modules, due to Serre and Pink-Ruetsche, respectively. Our approach is to prove a general result for certain Galois modules, which applies simultaneously to elliptic curves and to Drinfeld modules.

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Florian Breuer. 2008-10-17. Torsion bounds for elliptic curves and Drinfeld modules. https://arxiv.org/abs/0810.3147

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