2-ADIC INTEGRAL CANONICAL MODELS

Wansu Kim,Keerthi Madapusi Pera

doi:10.1017/fms.2016.23

Wansu Kim, Keerthi Madapusi Pera

Open Access

https://doi.org/10.1017/fms.2016.23

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Abstract

We use Lau’s classification of 2-divisible groups using Dieudonné displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial.

Highlights

We complete the construction of integral canonical models from [13] at places of hyperspecial level, so that it works at 2-adic places, without any additional restrictions
Let ShK (G, X ) be a Shimura variety of abelian type associated with a Shimura datum (G, X ) and a neat level K ⊂ G(A f ), defined over the reflex field E = E(G, X )
For a general Shimura datum of abelian type, the theorem is deduced from the case of Hodge type using Kisin’s twisting construction [13, Section 3]; see especially [13, Corollary 3.4.14]

Summary

Introduction

We complete the construction of integral canonical models from [13] at places of hyperspecial level, so that it works at 2-adic places, without any additional restrictions. These results will find use in a joint project of the second author with Andreatta, Goren and Howard on an averaged version of the Colmez conjecture on heights of abelian varieties with complex multiplication [2]. For any other possibly unfamiliar notions, we refer the reader to [12, Appendix] and [13, Section 1.1]

Lau’s classification and integral p-adic Hodge theory

Integral canonical models