On reduction of moduli schemes of abelian varieties with definite quaternion multiplications

Yu, Chia-Fu

Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 539-613.

Dans cet article, nous faisons une étude initiale sur les espaces de modules de type D en caractéristique positive $p\ne 2$, où le nombre premier $p$ peut être ramifié dans la donnée définissant l’espace de modules. Nous classifions explicitement les classes d’isogénie des groupes $p$-divisibles avec structures supplémentaires en question. Nous étudions également la réduction des espaces de modules de type D de rang minimal.

In this paper we make an initial study on type D moduli spaces in positive characteristic $p\ne 2$, where we allow the prime $p$ to ramify in the defining datum. We classify explicitly the isogeny classes of $p$-divisible groups with additional structures in question. We also study the reduction of the type D moduli spaces of minimal rank.

Classification : 14G35, 11G18
Keywords: Shimura varieties of type D, bad reduction, isocrystals
Mot clés : variétés de Shimura de type D, mauvaise réduction, isocristaux

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