Modular Curves as Shimura Variety

2013 ◽  
pp. 281-334
Author(s):  
Haruzo Hida
Keyword(s):  
Shimura Variety ◽  
Modular Curves

scholarly journals On the genus of some modular curves of level N

1996 ◽  
Vol 54 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Chang Heon Kim ◽  
Ja Kyung Koo
Keyword(s):  
Modular Curves

We estimate the genus of the modular curves X1(N).

Zeta functions of twisted modular curves

2006 ◽  
Vol 80 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Cristian Virdol
Keyword(s):  
Zeta Function ◽  
Galois Group ◽  
Complex Plane ◽  
Zeta Functions ◽  
Modular Curves ◽  
Absolute Galois Group ◽  
Modular Curve ◽  
The Absolute

AbstractIn this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.

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 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

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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