scholarly journals The supersingular locus of the Shimura variety of GU(1,n−1) II

2010 ◽  
Vol 184 (3) ◽  
pp. 591-627 ◽  
Author(s):  
Inken Vollaard ◽  
Torsten Wedhorn
Keyword(s):  
Shimura Variety

Corrigendum to the article On the supersingular locus of the GU(2,2) Shimura variety

2021 ◽  
Vol 15 (1) ◽  
pp. 307-308
Author(s):  
Benjamin Howard ◽  
Georgios Pappas
Keyword(s):  
Shimura Variety

scholarly journals On Goren–Oort stratification for quaternionic Shimura varieties

2016 ◽  
Vol 152 (10) ◽  
pp. 2134-2220 ◽  
Author(s):  
Yichao Tian ◽  
Liang Xiao
Keyword(s):  
Line Bundle ◽  
Real Field ◽  
Necessary Condition ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Maximal Level ◽  
Totally Real ◽  
Totally Real Field

Let $F$ be a totally real field in which a prime $p$ is unramified. We define the Goren–Oort stratification of the characteristic-$p$ fiber of a quaternionic Shimura variety of maximal level at $p$. We show that each stratum is a $(\mathbb{P}^{1})^{r}$-bundle over other quaternionic Shimura varieties (for an appropriate integer $r$). As an application, we give a necessary condition for the ampleness of a modular line bundle on a quaternionic Shimura variety in characteristic $p$.

scholarly journals GALOIS CONJUGATES OF SPECIAL POINTS AND SPECIAL SUBVARIETIES IN SHIMURA VARIETIES

2019 ◽  
pp. 1-15
Author(s):  
Martin Orr
Keyword(s):  
Special Point ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Canonical Models ◽  
Special Points

Let $S$ be a Shimura variety with reflex field $E$ . We prove that the action of $\text{Gal}(\overline{\mathbb{Q}}/E)$ on $S$ maps special points to special points and special subvarieties to special subvarieties. Furthermore, the Galois conjugates of a special point all have the same complexity (as defined in the theory of unlikely intersections). These results follow from Milne and Shih’s construction of canonical models of Shimura varieties, based on a conjecture of Langlands which was proved by Borovoi and Milne.

The GL4 Rapoport–Zink Space

2020 ◽  
Author(s):  
Maria Fox
Keyword(s):  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Connected Components ◽  
Shimura Variety ◽  
Irreducible Components

Abstract We give a description of the $\textrm{GL}_4$ Rapoport–Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl–Oort stratification. As an application of this, we also give a description of the supersingular locus of the Shimura variety for the group $\textrm{GU}(2,2)$ over a prime split in the relevant imaginary quadratic field.

Nearby cycles of automorphic étale sheaves

2017 ◽  
Vol 154 (1) ◽  
pp. 80-119 ◽  
Author(s):  
Kai-Wen Lan ◽  
Benoît Stroh
Keyword(s):  
Characteristic Zero ◽  
Shimura Variety ◽  
Etale Cohomology ◽  
Nearby Cycles ◽  
Étale Cohomology

We show that the automorphic étale cohomology of a (possibly noncompact) PEL-type or Hodge-type Shimura variety in characteristic zero is canonically isomorphic to the cohomology of the associated nearby cycles over most of their mixed characteristics models constructed in the literature.

scholarly journals Local models in the ramified case. III Unitary groups

2009 ◽  
Vol 8 (3) ◽  
pp. 507-564 ◽  
Author(s):  
G. Pappas ◽  
M. Rapoport
Keyword(s):  
Local Structure ◽  
Level Structure ◽  
Quadratic Extension ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Flag Varieties ◽  
Shimura Variety ◽  
Local Models ◽  
Affine Flag

AbstractWe continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primespat which the group defining the Shimura variety ramifies. We describe ‘good’p-adic integral models of these Shimura varieties and study their étale local structure. In the present paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties that we developed in a previous paper.

variety to a smaller Shimura variety

1998 ◽  
Vol 95 (1) ◽  
pp. 51-106 ◽  
Author(s):  
L. Clozel ◽  
T. N. Venkataramana
Keyword(s):  
Shimura Variety
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