Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves

Stanojkovski M, Voll C (2021)
Mathematische Annalen.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Stanojkovski, Mima; Voll, ChristopherUniBi
Abstract / Bemerkung
We describe the automorphism groups of finite p-groups arising naturally via Hessian determinantal representations of elliptic curves defined over number fields. Moreover, we derive explicit formulas for the orders of these automorphism groups for elliptic curves of j-invariant 1728 given in Weierstrass form. We interpret these orders in terms of the numbers of 3-torsion points (or flex points) of the relevant curves over finite fields. Our work greatly generalizes and conceptualizes previous examples given by du Sautoy and Vaughan-Lee. It explains, in particular, why the orders arising in these examples are polynomial on Frobenius sets and vary with the primes in a nonquasipolynomial manner.
Erscheinungsjahr
2021
Zeitschriftentitel
Mathematische Annalen
ISSN
0025-5831
eISSN
1432-1807
Page URI
https://pub.uni-bielefeld.de/record/2950122

Zitieren

Stanojkovski M, Voll C. Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen. 2021.
Stanojkovski, M., & Voll, C. (2021). Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen. https://doi.org/10.1007/s00208-021-02193-8
Stanojkovski, M., and Voll, C. (2021). Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen.
Stanojkovski, M., & Voll, C., 2021. Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen.
M. Stanojkovski and C. Voll, “Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves”, Mathematische Annalen, 2021.
Stanojkovski, M., Voll, C.: Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen. (2021).
Stanojkovski, Mima, and Voll, Christopher. “Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves”. Mathematische Annalen (2021).

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arXiv: 1912.09860

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