Norm-compatible systems of cohomology classes for GU(2,2)

2019 ◽  
Vol 16 (03) ◽  
pp. 461-510
Author(s):  
Antonio Cauchi
Keyword(s):  
Shimura Varieties ◽  
Shimura Variety ◽  
Modular Curve ◽  
Etale Cohomology ◽  
Étale Cohomology

We describe work of Faltings on the construction of étale cohomology classes associated to symplectic Shimura varieties and show that they satisfy certain trace compatibilities similar to the ones of Siegel units in the modular curve case. Starting from those, we construct a two-variable family of trace compatible classes in the cohomology of a unitary Shimura variety.

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 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 $p$.

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