Weak Néron models for cubic polynomial maps over a non-Archimedean field

Jean-Yves Briend (1) , Liang-Chung Hsia (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 NTNU - National Taiwan Normal University

The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field has a weak N\'{e}ron model or not.

Mots clés: weak Néron model; non-Archimedean dynamics; repelling fixed points; Julia set

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]

Jean-Yves Briend, Liang-Chung Hsia. Weak Néron models for cubic polynomial maps over a non-Archimedean field. Acta Arithmetica, 2012, 153 (4), pp.415-428. ⟨10.4064/aa153-4-5⟩. ⟨hal-01311138⟩