Shimura Curves within the Locus of Hyperelliptic Jacobians in Genus 3: Table 1.

2015 ◽  
Vol 2016 (6) ◽  
pp. 1603-1639 ◽  
Author(s):  
Samuel Grushevsky ◽  
Martin Möller
Keyword(s):  
Shimura Curves ◽  
Hyperelliptic Jacobians

scholarly journals On the Bloch–Kato conjecture for Hilbert modular forms

2021 ◽  
Author(s):  
Matteo Tamiozzo
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Euler System ◽  
Central Point ◽  
Shimura Curves ◽  
Hilbert Modular Forms ◽  
Reciprocity Laws ◽  
Hilbert Modular ◽  
Special Points

AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

scholarly journals Intersection Numbers of Heegner Divisors on Shimura Curves

2008 ◽  
Vol 4 (4) ◽  
pp. 1165-1204
Author(s):  
Kevin Keating ◽  
David P. Roberts
Keyword(s):  
Shimura Curves ◽  
Intersection Numbers

scholarly journals Reduction modulo 𝔓 of Shimura curves

1981 ◽  
Vol 10 (2) ◽  
pp. 209-238 ◽  
Author(s):  
Yasuo MORITA
Keyword(s):  
Shimura Curves ◽  
Reduction Modulo

scholarly journals Diagrams in the mod p cohomology of Shimura curves

2021 ◽  
Vol 157 (8) ◽  
pp. 1653-1723
Author(s):  
Andrea Dotto ◽  
Daniel Le
Keyword(s):  
Shimura Curves ◽  
Shimura Curve ◽  
Langlands Program ◽  
Mod P

Abstract We prove a local–global compatibility result in the mod $p$ Langlands program for $\mathrm {GL}_2(\mathbf {Q}_{p^f})$ . Namely, given a global residual representation $\bar {r}$ appearing in the mod $p$ cohomology of a Shimura curve that is sufficiently generic at $p$ and satisfies a Taylor–Wiles hypothesis, we prove that the diagram occurring in the corresponding Hecke eigenspace of mod $p$ completed cohomology is determined by the restrictions of $\bar {r}$ to decomposition groups at $p$ . If these restrictions are moreover semisimple, we show that the $(\varphi ,\Gamma )$ -modules attached to this diagram by Breuil give, under Fontaine's equivalence, the tensor inductions of the duals of the restrictions of $\bar {r}$ to decomposition groups at $p$ .

scholarly journals Betti numbers of Shimura curves and arithmetic three-orbifolds

2019 ◽  
Vol 13 (10) ◽  
pp. 2359-2382 ◽  
Author(s):  
Mikołaj Frączyk ◽  
Jean Raimbault
Keyword(s):  
Betti Numbers ◽  
Shimura Curves
Sign in / Sign up

Export Citation Format

Share Document