Finiteness criteria and uniformity of integral sections in some families of abelian varieties

DOI10.1007/s10711-023-00799-7arXiv1912.02930OpenAlexW2993191899MaRDI QIDQ6163396

Xuan Kien Phung

Publication date: 9 June 2023

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02930

zbMATH Keywords

abelian varietiesuniformityintegral pointsfiniteness criteriongeneric emptiness

Mathematics Subject Classification ID

Rational points (14G05) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Abelian varieties of dimension (> 1) (11G10) Divisors, linear systems, invertible sheaves (14C20) Algebraic theory of abelian varieties (14K05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The canonical height and integral points on elliptic curves
• Integer points and the rank of Thue elliptic curves
• Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces
• On the torsion values for sections of an elliptic scheme
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
• Rational Points of Abelian Varieties Over Function Fields
• Néron Models
• Bounds for curves in abelian varieties
• FAMILIES OF ALGEBRAIC CURVES WITH FIXED DEGENERACIES
• Uniformity of rational points
• Abelian Varieties Over Function Fields
• ON ABELIAN VARIETIES OVER FUNCTION FIELDS
• The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume I
• On the Parshin-Arakelov theorem and integral sections on elliptic surfaces