# Integral canonical models of Shimura varieties

@article{Kisin2009IntegralCM, title={Integral canonical models of Shimura varieties}, author={Mark Kisin}, journal={Journal de Theorie des Nombres de Bordeaux}, year={2009}, volume={21}, pages={301-312} }

Le but de cette note est de fournir une introduction a la theorie des modeles entiers canoniques des varietes de Shimura, et de donner une esquisse de la preuve d'existence de tels modeles pour les varietes de Shimura de type Hodge, et plus generalement, de type abelien. Pour plus de details, le lecteur est renvoye a [Ki 3].

## 22 Citations

### Geometry of Shimura varieties of Hodge type over finite fields

- Mathematics
- 2007

We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of in-…

### Three methods to prove the existence of integral canonical models of Shimura varieties of Hodge type

- Mathematics
- 2008

This is a survey of the three main methods developed in the last 15 years to prove the existence of integral canonical models of Shimura varieties of Hodge type. The only new part is formed by…

### TOWARDS A DEFINITION OF SHIMURA CURVES IN POSITIVE CHARACTERISTICS

- Mathematics
- 2014

In this paper, we seek an appropriate denition of Shimura curves of Hodge type in positive characteristics. The basic idea is to characterize the reduction of Shimura curves. Speci- cally, we study…

### Toroidal compactifications of integral models of Shimura varieties of Hodge type

- Mathematics
- 2012

We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type that parameterize isogenies of abelian varieties with additional structure. We also construct…

### The trace formula and the existence of PEL type Abelian varieties modulo p

- Mathematics
- 2012

We show, using the trace formula, that any Newton stratum of a Shimura variety of PEL-type of types (A) and (C) is non-empty at the primes of good reduction. Furthermore we prove conditionally the…

### Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport

- Mathematics
- 2007

We state an improved version of the conjecture of Langlands and Rapoport, and we prove the conjecture for a large class of Shimura varieties. In particular, we obtain the first proof of the…

### TOWARDS A DEFINITION OF SHIMURA CURVES IN POSITIVE CHARACTERISTICS

- Mathematics
- 2014

In this paper, we seek an appropriate definition of Shimura curves of Hodge type in positive characteristics. The basic idea is to characterize the reduction of Shimura curves. Specifically, we study…

### The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type

- Mathematics
- 2014

We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the…

### The geometric and arithmetic volume of Shimura varieties of orthogonal type

- Mathematics
- 2011

We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the…

### Seed Relations for Eichler--Shimura congruences and Euler systems

- Mathematics
- 2021

This paper proves that the U-operator [Bou21d] attached to a cocharacter is a right root of the corresponding Hecke polynomial. This result is an important ingredient in the proof of (i) the…

## References

SHOWING 1-10 OF 24 REFERENCES

### Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant

- Mathematics
- 1994

© Foundation Compositio Mathematica, 1994, tous droits reserves. L’acces aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…

### Integral Canonical Models of Shimura Varieties of Preabelian Type

- Mathematics
- 1999

We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.

### A motivic conjecture of Milne

- Mathematics
- 2003

Let k be an algebraically closed field of characteristic p>0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates, in the case of abelian…

### Modularity of 2-adic Barsotti-Tate representations

- Mathematics
- 2009

We prove a modularity lifting theorem for two dimensional, 2-adic, potentially Barsotti-Tate representations. This proves hypothesis (H) of Khare-Wintenberger, and completes the proof of Serre’s…

### Integral models for Shimura varieties of abelian type

- Mathematics
- 2010

Introduction 967 1. Reductive groups and p-divisible groups 971 (1.1) Cocharacters and filtrations 971 (1.2) Review of S-modules 973 (1.3) Reductive groups and crystalline representations 975 (1.4)…

### On the conjecture of Langlands and Rapoport

- Mathematics
- 2007

FORENOTE (2007): The remarkable conjecture of Langlands and Rapoport (1987) gives a purely group-theoretic description of the points on a Shimura variety modulo a prime of good reduction. In an…

### Some Contemporary Problems with Origins in the Jugendtraum

- Mathematics
- 2001

The twelfth problem of Hilbert reminds us, although the reminder should be unnecessary, of the blood relationship of three subjects which have since undergone often separate developments. The first…

### Canonical Models of (Mixed) Shimura Varieties and Automorphic Vector Bundles

- Mathematics
- 2002

The article surveys what was known, or conjectured, about canonical models of Shimura varieties and related objects at the time it was written (1988). I Abelian varieties with complex multiplication…

### The points on a Shimura variety modulo a prime of good reduction

- Materials Science
- 1992

In the known process of manufacturing an amphoteric polymeric composition which process comprises firstly polymerising a mixture comprising a monomer containing a basic group and a monomer containing…