Plane quartics over Q with complex multiplication

Abstract : We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.
Type de document :
Pré-publication, Document de travail
2017-13. 34 pages. 2017
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https://hal.archives-ouvertes.fr/hal-01455036
Contributeur : Marie-Annick Guillemer <>
Soumis le : vendredi 3 février 2017 - 11:10:10
Dernière modification le : samedi 23 septembre 2017 - 01:10:09

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  • HAL Id : hal-01455036, version 1
  • ARXIV : 1701.06489

Citation

Pinar Kilicer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, et al.. Plane quartics over Q with complex multiplication. 2017-13. 34 pages. 2017. 〈hal-01455036〉

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