A tubular variant of Runge's method in all dimensions, with applications to integral points on Siegel modular varieties

DOI10.2140/ant.2019.13.159zbMath1448.11119arXiv1611.09054OpenAlexW3100744020WikidataQ128310275 ScholiaQ128310275MaRDI QIDQ1732981

Samuel Le Fourn

Publication date: 26 March 2019

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09054

zbMATH Keywords

abelian varietiesRunge's methodintegral points on varieties

Mathematics Subject Classification ID

Rational points (14G05) Abelian varieties of dimension (> 1) (11G10) Varieties over global fields (11G35) Modular and Shimura varieties (14G35)

Related Items

On Runge's method and the integral points of some modular varieties, Tubular approaches to Baker's method for curves and varieties, Bounding integral points on the Siegel modular variety \(A_2(2)\), Extending Runge’s method for integral points

Cites Work

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• Surjectivity of Galois representations associated with quadratic \(\mathbb {Q}\)-curves
• Lower bound of the Néron-Tate height on abelian surfaces
• Integral points on threefolds and other varieties
• Siegel modular forms of degree 2 over rings
• Variations on a theme of Runge: effective determination of integral points on certain varieties
• Arithmetic distance functions and height functions in diophantine geometry
• Toroidal compactification of Siegel spaces
• On the geometry of a Siegel modular threefold
• Stable genus 2 curves and their moduli scheme
• Minorations des hauteurs normalisées des sous-variétés de variétés abeliennes. II. (Lower bounds for normalized heights of subvarieties of Abelian varieties. II.)
• Effective analysis of integral points on algebraic curves
• Bounds for the torsion of elliptic curves over number fields
• On Runge's method and the integral points of some modular varieties
• On the equations defining Abelian varieties. I-III
• Arithmetic variety of moduli for genus two
• The Siegel modular variety of degree two and level three
• Torsion points on theta divisors
• Theta height and Faltings height
• Cartier and Weil divisors on varieties with quotient singularities
• Runge's Method and Modular Curves
• On Weil's "Theoreme de Decomposition
• The Picard group of Siegel modular threefolds.
• Examples of torsion points on genus two curves
• On the Graded Ring of Theta-Constants (II)
• Modular Forms and Projective Invariants
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura