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 Bounded negativity of self-intersection numbers of Shimura curves in Shimura surfaces

2015 ◽  
Vol 9 (4) ◽  
pp. 897-912 ◽  
Author(s):  
Martin Möller ◽  
Domingo Toledo
Keyword(s):  
Shimura Curves ◽  
Intersection Numbers ◽  
Shimura Surfaces

THE JACQUET–LANGLANDS CORRESPONDENCE AND THE ARITHMETIC RIEMANN–ROCH THEOREM FOR POINTED CURVES

2012 ◽  
Vol 08 (01) ◽  
pp. 1-29 ◽  
Author(s):  
GERARD FREIXAS I MONTPLET
Keyword(s):  
Modular Forms ◽  
Shimura Curves ◽  
Intersection Numbers ◽  
Shimura Curve ◽  
Langlands Correspondence ◽  
Modular Curve ◽  
Roch Theorem ◽  
Petersson Norms

We show how the Jacquet–Langlands correspondence and the arithmetic Riemann–Roch theorem for pointed curves, relate the arithmetic self-intersection numbers of the sheaves of modular forms — with their Petersson norms — on modular and Shimura curves: these are equal modulo ∑l∈S ℚ log l, where S is a controlled set of primes. These quantities were previously considered by Bost and Kühn (modular curve case) and Kudla–Rapoport–Yang and Maillot–Roessler (Shimura curve case). By the work of Maillot and Roessler, our result settles a question raised by Soulé.

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

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.

Intersection Numbers for Twisted Homology

2004 ◽  
Vol 114 (2) ◽  
Author(s):  
Toyoshi Togi
Keyword(s):  
Intersection Numbers ◽  
Twisted Homology

scholarly journals Automorphic forms and cohomology theories on Shimura curves of small discriminant

2010 ◽  
Vol 225 (2) ◽  
pp. 1013-1045 ◽  
Author(s):  
Michael Hill ◽  
Tyler Lawson
Keyword(s):  
Automorphic Forms ◽  
Shimura Curves
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