Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\)

DOI10.5802/jtnb.862zbMath1308.14027arXiv1212.1294OpenAlexW2963678220WikidataQ125703462 ScholiaQ125703462MaRDI QIDQ2454449

Hartwig Mayer

Publication date: 13 June 2014

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.1294

zbMATH Keywords

modular curverelative dualizing sheafArakelov self-intersection number

Mathematics Subject Classification ID

Modular and Shimura varieties (14G35) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (7)

The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf ⋮ An effective Arakelov-theoretic version of the hyperbolic isogeny theorem ⋮ Arakelov self-intersection numbers of minimal regular models of modular curves \(X_0(p^2)\) ⋮ Bounds for canonical Green's function at cusps ⋮ Semi-stable models of modular curves \(X_0(p^2)\) and some arithmetic applications ⋮ The effective Shafarevich conjecture for abelian varieties of -type ⋮ Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Admissible pairing on a curve
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Calculus on arithmetic surfaces
• La formule de Noether pour les surfaces arithmétiques. (The Noether formula for arithmetic surfaces)
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Twists of newforms and pseudo-eigenvalues of \(W\)-operators
• Points of small height on the modular curves \(X_0(N) \)
• The Rankin-Selberg method on congruence subgroups
• Two theorems on modular curves
• Bounds on Faltings's delta function through covers
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• Bounds for special values of Selberg zeta functions of Riemann surfaces
• Computational Aspects of Modular Forms and Galois Representations
• Eisenstein Series and the Selberg Trace Formula. II
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
• Bounds on canonical Green's functions

This page was built for publication: Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\)