# ANNALES DE L'INSTITUT FOURIER

The Relative Canonical Ideal of the Kummer–Artin Schreier–Witt family of curves
Annales de l'Institut Fourier, Volume 73 (2023) no. 3, pp. 1085-1113.

We study the canonical model of the Kummer–Artin Schreier–Witt flat family of curves over a ring of mixed characteristic. We first prove the relative version of a classical theorem by Petri, then use the model proposed by Bertin–Mézard to construct an explicit generating set for the relative canonical ideal. As a byproduct, we obtain a combinatorial criterion for a set to generate the canonical ideal, applicable to any curve satisfying the assumptions of Petri’s theorem, except for plane quintics and trigonal curves.

Nous étudions le modèle canonique de la famille de courbes plate de Kummer–Artin Schreier–Witt sur un anneau de caractéristique mixte. Nous prouvons d’abord la version relative d’un théorème classique de Petri, puis utilisons le modèle proposé par Bertin–Mézard afin de construire un ensemble de générateurs explicite de l’idéal canonique relatif. De plus, nous obtenons un critère combinatoire pour qu’un ensemble engendre l’idéal canonique, applicable à toute courbe satisfaisante les hypothèses du théorème de Petri, á l’exception des planes quintiques et des courbes trigonales.

Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3543
Classification: 14H10, 14F10
Keywords: Relative curves, Canonical ideal, Reduction and Lifting
Mot clés : Courbes relatives, idéal canonique, réduction et relèvement
Charalambous, Hara 1; Karagiannis, Kostas 1; Kontogeorgis, Aristides 2

1 Department of Mathematics Aristotle University of Thessaloniki School of Sciences 54124, Thessaloniki (Greece)
2 Department of Mathematics National and Kapodistrian University of Athens Panepistimioupolis 1 5784 Athens (Greece)
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Charalambous, Hara; Karagiannis, Kostas; Kontogeorgis, Aristides. The Relative Canonical Ideal of the Kummer–Artin Schreier–Witt family of curves. Annales de l'Institut Fourier, Volume 73 (2023) no. 3, pp. 1085-1113. doi : 10.5802/aif.3543. https://aif.centre-mersenne.org/articles/10.5802/aif.3543/

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