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…
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