Abstract
A quasiplatonic curve can be defined over the rationals if it has a regular dessin with abelian automorphism group.
Dedicated to the memory of Wolfgang Schwarz
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Notes
- 1.
Both authors were supported by the DFG project Wo 199/4–1.
- 2.
Girondo et al. [6] contains a little mistake: since β is used in the base field of the Galois extension of function fields, we have to be sure that β is also defined over the field of constants; this is guaranteed here by the construction of K ≤ L . In Corollary 1 of [6] this may fail if the hypotheses of Lemma 1 or Lemma 2 of [6] are not satisfied. There one can fill the gap in the hypothesis by replacing the moduli field M(S, G) with a—sometimes slightly larger—moduli field M(S, β, G) in whose definition all f σ satisfy in addition β σ ∘ f σ = β .
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Wolfart, J., Mühlbauer, B. (2016). Regular Dessins with Abelian Automorphism Groups. In: Sander, J., Steuding, J., Steuding, R. (eds) From Arithmetic to Zeta-Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-28203-9_32
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